If multiple users sharing the calendars among them invite each other, each user sees multiple occurrences of the same event. All are displayed as very narrow entries with pretty much no information readable.

It would be more reasonable to print one of them in large (with contents readable) and only indicate the existence of the others by very narrow bars. For events with invitations, the connection between them should be easily recognizable as they share the same UUID.

Of course, the problem also exists with multiple unconnected events at the same time slot, but there's nothing that really could be changed here. Multiple copies of the same event occur very often for some of our users, and there is a reasonable semantics behind determining the "most important" event (your own/the one from the first calendar in the calendar list).