BLUF: There is no centralized data on transmission problems (trust me, I looked extensively before purchasing my JK), all due to the manufacturer.
I've been a Chevy guy since I was 15, bought and sold 5 different models from '01 to '09. On every one of them (trucks and a Z06), there was a database that the dealership could access to answer your exact kind of question. For example, some '02 and '03 Z06 models had faulty valve-springs, but there was no official recall. I took mine into a dealer to see if they could tell me more, and they ran my VIN vs. other Z06's that had been brought to the Goodwrench guys across the country and we figured out I was in the clear because of my assembly date.
Now, compare that to my experience with Chrysler. I called a dealership before I went to TN to pick up my JK last week and asked "I have a VIN #, Carfax says there is 1 open recall on it, can you tell me what the recall is?" Maybe it is because I live in MS and incompetence runs rampant in this state, but the tech I spoke to at the dealership said "......uh..... no".
I'll spare you the details on the rest of the conversation, but we talked about the transmission problem as well. I think I've seen a TSB about the whole ordeal (somewhere on this forum), but nobody at the dealership will confirm or deny the existence of a manual transmission problem. It appears to be hit or miss though, because my '08 doesn't show any signs of transmission trouble.