The dialog box in question here is the one you get with the context menu option "open with other applications". Wine seems to have inserted more than a dozen or so entries for each application I install, which makes it a pain to find the correct application:

What can I do to remove the duplicates?

Update: Neither of the two solutions really work. The bug is interesting, but the symptoms does not match my problem (I'm not having problem with uninstalling applications, but rather the things that are inserted after installing them), and with the other one, all references to the Wine application are removed, which actually makes the problem worse (although it may be an acceptable solution if nothing else can be found). So this is still an open question; any takers?