[Author's note: I don't think this is that well-written, given that I didn't have much time to put into it. But I think my final idea should be implemented, because so many foreigners (and probably natives) in Japan would take advantage of it.]
It is difficult to look up kanji in a paper-based dictionary. Plainly and simply, one spends a considerable time on the process of flipping through pages and searching through characters. If the method of kanji search is by stroke order, one must know the number of strokes in every character. Although stroke order is a prerequisite to writing kanji, difficult characters with many strokes remain confusing, especially to those persons who frequently consult a dictionary (ie., students). If the method of kanji search is by radical, one must look up the radical, turn to its page, then search for the illusive kanji by browsing through all of the characters with the same corresponding radical. The dictionary user must also understand the concept of primary and secondary radicals, if the character contains more than one radical. For example, the Japanese kanji for farm or field, 畑 (はた), is composed of two radicals; however, the primary radical with which to search for 畑 in a dictionary is not 火 but 田 (though at first glance, one would assume the primary radical to be the radical on the left). Although books are still in print and circulation, in such a technological age, the retention of paper-based kanji dictionaries remains open to debate. With modern computing hard- and software, the exercise of spending minutes flipping through pages is outdated.
Enter the electronic dictionary. The patent for the English-language QWERTY keyboard layout was filed in 1867 [1] and was later transfered to the modern computer keyboard. The Japanese computer keyboard utilizes the same lettering layout as the English version; however, hiragana characters are laid out on the same English-letter keys, as well as the number keys and a few punctuation keys. Separate punctuation keys are assigned to the Japanese 濁点 (だくてん) and 半濁点 (はんだくてん), the dotted and circular diacritical marks. Japanese input on an English-language QWERTY keyboard follows the Romaji system [2], similar to the Hepburn romanization [3] of the Japanese language, but with some additional exceptions (such as pressing “n” twice to print ん, or typing “gyo” for ぎょ, on screen). For kanji recognition to occur, pressing the space bar changes a previously-typed single or combination of hiragana characters into the corresponding kanji character or characters. Pressing the space bar a second time calls up different kanji combinations with the same reading, which the user must sort through to select.
Keyboard-based character composition still poses many difficulties. First, in regards to the readings of kanji, characters, found for instance first on a website and then copied and pasted into a text editor, cannot be converted into the characters’ corresponding hiragana reading. Second, and more troublesome, if a person does not know the reading of a kanji or set of kanji, he cannot input the hiragana to print the character on screen. Third, combining these two prior issues, if a person cannot read a kanji, then he must look it up in an online dictionary in the same fashion as in a paper-bound dictionary. Although slightly faster than scanning through pages, computer- or Internet-based dictionaries do not significantly speed up the process of looking up characters.
Enter handwriting recognition. Instead of searching through an unknown number of pages in a dictionary, be it digital or analog, handwriting recognition allows for quick to instant kanji searches. Today, the more-expensive handheld electronic dictionaries (電子辞書) come with a stylus and writing pad, while many online versions of handwriting recognition exist [4]. With modern touch-sensitive cellphones (like the iPhone), via use of the Japanese language setting, kanji can be handwritten on the screen and inputted into a dictionary. One of the more practical applications of handwriting recognition has materialized in the form of the Nintendo DS gaming system. With a stylus and dual-touch screen, the DS boasts many language learning games, such as Minna no DS Seminar: Kanpeki Kanji Ryoku [5] or Kanji Sonomama DS Rakubiki Jiten [6].
The latter of these two games, Kanji Sonomama, acts as an electronic dictionary on the portable DS platform. The software allows users to look up entries in either English or Japanese with a handwritten recognition system for English lettering, numbers, hiragana, katakana, and kanji. Character palettes can be chosen for each alphabet; however, two squares, both split by horizontal and vertical lines, are available for written character entry. Once a character is written, a small book-like image flips its pages to the place in the electronic dictionary containing the kanji (or English word) related to the written figures. For example, when て is entered, the first entry that appears is 手; then, when る is written, the book flips an assortment of listings, starting with 照る (てる).
The problem with handwritten character recognition is obvious: human error. Not everyone’s handwriting is perfect, not everyone’s stroke order in tune. The horizontal and vertical division of the blocks echoes practice sheets for Japanese character penmanship, but it also allows the system to place beginning and ending points for the written lines of radicals, characters, letters, and numbers. Sometimes the system believes the intended written character to be another, but the user is given options to choose between “漢字” (where the software searches for all characters, letters, numbers, etc.), “かな” (to search for only hiragana), “カナ” (for only katakana), “英字” (for English letters), and “数字” (for numbers), to allow for a refined recognition and to speed up searches. When the system picks an incorrect character, the user is also allowed the option of choosing eight of the most similar characters to the figure recognized by the software.
It is not unusual for the Kanji Sonomama program to make mistakes. In fact, the more simple characters produce the most random results. Unless 子 is written into the system well, it might come out as either 孑, 孒, or even コ. The system mandates a good sense of stroke order and an awareness of penmanship. Games such as Sonomama seem the solution (as a type of “exam”) to any complaints about failure of penmanship in the academic system.
The question for scientists is how to create software that analyses handwriting to create better character recognition. Toru Wakahara and Kazumi Odaka propose three problems with the recognition system: “stroke-number and stroke-order free recognition, robustness against handwriting distortion, and discrimination between similarly shaped but different Kanji characters” [7]. Basically, the duo identify that 1) recognition must be based on stroke number and order, 2) personal styles of handwriting create error, and 3) the systems usually mistake kanji that look very similar. Their research emphasizes the necessity of the stroke, “the most basic structural unit in Kanji character composition” [8], in education, because software (also manmade, like the writing system) depends on students’ proper penmanship. Their research focuses mainly on the second of the three problems they point out, penmanship distortion, and they try to resolve the issue by overlaying reference patterns (a two-layer process) for kanji characters on top of the written characters inputted by the user. The results of their research affirms an interesting fact: that kanji with less characters are more likely to turn up errors (see the errors associated with 子 above).
At the University of Tokyo, Ikumi Ota and his three colleagues also have performed research in relation to character recognition [9]. Based on the relative position of characters in a set of kanji (“Kanji string”), their research focuses on the style of handwritten kanji by measuring vectors (the distance) between the corner points of a box drawn around radicals and full characters. The string that the software analyses breaks apart a kanji into its radicals and then its strokes, so that, again, the stroke is emphasized as the most important part of the character. The problem with their research is that in the end radicals were occasionally identified as separate kanji altogether (eg., 短 transformed into 矢 and 豆) or two kanji were combined into one (eg., 一人 becoming 大), ultimate understood by the program in a general sense as really bad handwriting). Whether a success or failure, their research continues to emphasize that when learning and writing kanji, stroke order and penmanship remains a key element.
In today’s world of technological innovation, what is the future of kanji recognition? Enter image recognition. A recent start-up called Evernote [10] allows users to take pictures of everyday objects, such as signs, book covers, or their own handwriting, and store them as “notes” in their account to browse when time permits, Along with basic clips of text from the web, Evernote can search images by recognizing the text inside the pictures. If the software were adapted for Japanese language use, users could take pictures of kanji in signs and books; then, the software could match the kanji in the picture to a reference set of characters and reproduce the hiragana reading and dictionary meaning for the user. As an education tool, such a system would bypass the time needed to write a kanji into a dictionary, creating an instantaneous translation of the unknown word. The only drawback: the system no longer intrinsically emphasizes the necessity of good handwriting.
[1] http://en.wikipedia.org/wiki/QWERTY
[2] http://www.kictec.co.jp/inpaku/iken%20keikai/syasin/hebon/romaji.htm
[3] http://www.halcat.com/roomazi/doc/hep3.html
[4] A simple example: http://kanji.sljfaq.org/draw.html
[5] http://www.gamefaqs.com/portable/ds/home/933403.html
[6] http://www.gamefaqs.com/portable/ds/home/932301.html
[7] “On-Line Cursive Kanji Character Recognition Using Stroke-Based Affine Transformation.” Toru Wakahara & Kazumi Odaka. IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 19, No. 12, December 1997.
[8] Ibid.
[9] “On-Line Handwritten Kanji String Recognition Based on Grammar Description of Character Structures.” Ikumi Ota, Ryo Yamamoto, Takuya Nishimoto, & Shigeki Sagayama. IEEE, 2008.
[10] http://evernote.com

As a student of Mandarin I’ve struggled with a lot of the same issues you wrote about. Paper dictionaries are terribly cumbersome. Worse, the secondary order (after the radical is identified) changes from dictionary to dictionary. My PDA has stroke recognition sw that has increased lookup time dramatically.
Another fascinating topic is character input on cell phones. One system uses pinyin (much like the system you describe) and another is based entirely on entering the direction of strokes and selecting from a submenu. I totally appreciate the strictness of my early instructors w/r/t stroke order.
Also, my studies have made me really appreciate font development. The amount of work to create an asian font is unreal compared to roman character!
I actually forgot to comment about cell phone input! In Japan, hiragana is based upon a consonant followed by either a, i, u, e, or o. And there are enough beginning consonants that it fits perfectly on the number sequence of a cell phone, kind of like the English alphabet. So useful in fact that Japanese kids took typing on cell phones to such a new level that cell-phone layout USB keyboards became pretty popular across the country.