Only problem is that the script works only if I open vim with 'vim' and not with 'sudo vim' (by the way, why is that?).

Based on what you've said, I'm not sure if this is an sudo issue or a vim issue. Where is scriptname, and where are the files that scriptname references? Your sudoers may be set up to replace the environment in such a way that vim looks relative to root's home directory rather than your user's home directory. You may need to copy your ~/.vim directory to ~root/.vim, if ~/.vim is where you've put scriptname and the other things it loads. Or you can move these into a system-wide path that vim searches.