Hi Niels,
just noticed no one had replied to this...
Error: xelatex is not found, you need to install LaTeX or be sure that your PATH is setup properly.
sh: line 0: type: xelatex: not found
When I run from TextMate "which xelatex" it gives me: /usr/texbin/xelatex In Terminal the same, command completion in Terminal works fine as well. Compiling the file in Terminal works as well.
The PATH as set in a terminal window is not the PATH that TextMate sees. You can see what PATH is available in TextMate by entering
printenv PATH
and then (with the cursor on that line) hitting control-R. I imagine that you'll find "/usr/texbin" is *not* in the resulting list, so you need to get it in there. Section 8.2 of the TextMate manual covers how to do this...
http://manual.macromates.com/en/shell_commands#search_path
Good luck, Paul