Thanks for your reply! I did use the Conflicts Test guide, and found that the theme was no problem (although based on the old 2010 theme).
Then all plugins deactivated, except the Event Calendar ones of course – and “Theme Test Drive”, that I had to use so our reders wouldn’t be too confused. Also deleted Log in Safari.
After several reloads, the Form finally went back to the normal view, with the events and arranger fields perfect!
I re-activated the plugins, and it seems that “WP Edit” was the culprit (haven’t tried to activate it again though, so cannot say 100% for sure).
Thanks Victor!