An e-mail:

Kathryn, Thompson plays himself in Looking for Comedy. He has been brought on by the administration to work through the State Department on a new initiative to find out what makes Muslims laugh. Thompson has some humorous bits, mainly through his interaction with Albert Brooks, but he’s only in (I think) two scenes: when he first meets with Brooks and then at the end after Brooks’ trip. You can see some of the first scene in the trailer here.
Overall the movie was pretty funny.
By far, the movies Thompson wants to disavow are Baby’s Day Out and Die Hard 2. While he was pretty good in Die Hard 2 (haven’t seen Baby’s Day Out), the movie itself was a real stinker.