OS X Lion: app.log file in Applications Folder
Probably a bit sledgehammer-to-crack-a-nut, but if its happening fairly regularly and you can't figure out what's creating it another way, you could start a terminal prompt and leave the following command running

sudo opensnoop | grep -i app.log


This will monitor for app.log being created and tell you the process that created it (I'm assuming there won't be that many processes creating a file called app.log, but I guess you could narrow it down to /Applications if you wanted to). At least then you'll be armed with the knowledge of what is creating the file and can potentially do something about it.

For example, whilst running the above command, if you type

touch app.log


in another terminal tab or window, the original one running the opensnoop command displays

501  10576 touch          3 app.log              
501  10099 mdworker       6 /Users/binarybob/Documents/app.log