Calendar 6 and iOS7 iPhone Calendar don't snychronise correctly

Hello. Already with the last iOS (iOS 6, through all versions), synchronising between Desktop Mac (10.5.8 now) and iPhone Calendars never worked correctly: Events added on iPhone aren't transferred to Mac, Mac events are transferred to iPhone, but are doubled into the event itself and another often, but not always with the same hours, but always as an empty New Event.

Since the problem remains after a clean install of iOS7 with no restauration from backup and purely manual setup, I reckon the problem can't very well be in the phone, whence I think it should be the Calendar or something else on the Desktop side. Any idea?

Thanks a lot