Problem is solved: I added two lacking fields to the database and it works again!
I am now using version 5.1.3. I installed it on a fresh Joomla 3.3 website, which is now upgraded to 3.4.
Iam not sure about the earlier version of Matukio : I think it is 4.5.1.
I exported the table of the events and imported it into the new version, so that may have caused some troubles??
Until now there were no other issues discovered.