how to move the textmate file explorer to the right side?
You can move textmate to the left edge of the screen and close and open the panel. ie. ctrl, alt, cmd + d.
TextMate --> Preferences --> Projects --> Show file browser on: --> Left side / Right side
If you're not using ProjectPlus by Ciarán Walsh, I highly recommend it. It makes some small but helpful improvements to TextMate's project features. It also allows you to specify the default side for the project drawer (which actually becomes a nice panel).
If you have it installed, go to Preferences > Project+ > Sidebar and select "Show sidebar on the right side of the window".
Update:
For later versions of textmate, see this answer
For Textmate 2 (released long after this question was answered) the accepted answer doesn't appear to work anymore. This is what did it for me:
To change it to the right on OSX, open up your terminal and run the command:
defaults write com.macromates.TextMate.preview fileBrowserPlacement right
To change it to the left:
defaults write com.macromates.TextMate.preview fileBrowserPlacement left