My understanding is that under UK law, if you were to create your own word-lists based on examination of JLPT (or whatever) tests, then you own the copyright to that. I know that in the USA there is precedent for the creator of a word-list owning the copyright to that list, but that means only the complete list, as anyone can reasonably create a list of words conforming to certain conditions. The scrabble word lists have tested this in court.
So you will need to take into account the license for any data you plan to use. Jonathan Waller has JLPT word lists released under the CC-BY license, meaning you can use them commercially as long as he is given some credit somewhere.
Any translation service will be subject to terms of service, rather than copyright, and you'll need to study those for any service you plan to use.
The Google translate API is now a commercial (paid-for) service, as laid out in the TOS. You can use it for any sort of content, commercial or otherwise, unless it's to 'improve ... a substantially similar product or service', which basically means don't make your own translation website which secretly uses Google's. The TOS forbids any attempts to use the service whilst avoiding the fee-paying mechanism, which means you couldn't, for example, make HTTP requests to the translate web page and scrape the results. The prices are very fair, so you should consider signing up and paying - if you're using the API enough to incur big fees, your app should be making big money.
Dictionaries are certainly copyrightable in most countries which respect that sort of thing, being true creative works which involve generating new content and not just subsetting some other source. They will therefore always be under copyright unless the right have been waived by the author, and you'll need to look for a data license for each dictionary.
Online dictionaries generally have their own licenses published on their websites. For example, the licenses for JMDICT, ENAMDICT, KANJIDIC, etc. are under CC-BY SA license, as explained in full here. That means you can use them with attribution, including in commercial apps, but in this case they recommend (but don't require) making a small donation to the project if you do so. The SA part means Share-Alike, i.e. if you create a new list which is largely derived from the original one, you must release it under the same license (you don't have to release any software which uses the list under that license, though).
Last edited by Blahah (2012 May 10, 8:42 am)