Probably some javascript conflict. Where/how can I see the issue?

No idea... try switching on the Error Reporting in the Joomla configuration...

Otherwise, can you also give me admin and (s)ftp access so I can take a deeper look?

I can connect via ftp, but I seem to have no rights to edit any files.

Please try the latest development version from:
regularlabs.com/development-releases

The error could happen due to a temporary server issue during upload. Does it give the same error if you try to install it again?