This thread is interesting. I have an electronic dictionary that I bought a few years ago, so I mostly use the web-based dictionaries when I'm using my iPod Touch. I wasn't aware that there were dictionaries available for download and purchase.
By the way, which Chinese character set are you using for your input? I have the traditional and simplified Chinese handwriting input, so it covers close to all of the characters I would need, although most of the time I just copy and paste from websites (or I don't look up the word... that can get labor-intensive and annoying). Anyway, for 大学 you'd need the simplified set (traditional is 大學). It gets to be a problem when there are characters that were simplified differently in Japanese and on the mainland, but I'm not sure how many of those there are. I'd be interested to see examples of ones that you've had problems with (I know you'd have problems with 権, 観, 歓, 勧, for instance -- SC: 权, 观, 欢, 劝; TC: 權, 觀, 歡, 勸).