Why is there a duplicate entry for my TextMate?
Mac OS X automatically keeps a database of all applications and their corresponding file-types called the LaunchServices database. You can examine where both of your TextMate executables are located by opening Terminal.app from /Applications/Utilities and entering:

/System/Library/Frameworks/CoreServices.framework/Frameworks/LaunchServices.framework/Versions/A/Support/lsregister -dump |  /Applications/TextMate.app/Contents/Resources/mate


This will open a long file full of all Applications that your LaunchService DB "knows" on your Mac in TextMate. Examine this file for the "path:" of your duplicate entires of "TextMate". 

It´s quite likely that you´ve already removed the second "TextMate" but your LaunchServices still remembers it. I guess you should tell the Datatbase to rebuild by entering:

/System/Library/Frameworks/CoreServices.framework/Frameworks/LaunchServices.framework/Versions/A/Support/lsregister -kill -r -domain local -domain system -domain user


into the Terminal and then restarting your computer. This may lead to your Mac forgetting some custom "open with.." assignments though.