Probably the biggest one: You lose your keys; you lose your data. This deserves the most consideration and you need to have the best possible key management.
Also, if you plan on encrypting at the client level, that may cause some issues if you have implemented deduplicaiton within your environment. Deduplication technology needs to recognize identical data blocks or segments in order to work. If you start encrypting your data at the source to put it on tape, that will completely destroy your ability to apply deduplication. So that is something worth considering. You can not have both.
If you are encrypting at the device level, it takes care of that problem, but then you are not deduplicating on tape. So if you are deduplicating on disk, staging on disk or encrypting at the source, this is definitely an issue.
Check out the entire Tape Encryption FAQ.