What is the Problem with Apostrophes?

Even the BBC can trip up over the proper use of the apostrophe as witnessed in last week’s episode of Panorama entitled It Shouldn’t Happen at a Vets’. Watching film of the poor animals in distress was bad enough but the programme also included some captions in which this howler (no pun intended) appeared. On this occasion, and this seems to be a particular issue, the problem is the use of the apostrophe in its or it’s. The former is used to show possession, ie its name, its parents, etc, and the latter means simply that the second i has been omitted. An example of this is it’s going to rain; instead of saying, it is going to rain. Simple. So why is there such a problem with apostrophes? Answers on a postcard, please.