Miranda - Not true, the full stop is correct inside the quotation marks as that was the end of the sentence. Remember that all political speeches these days (since Blair) have to have really short sentences (often with no finite verb).
MirandaGoshawk, surely that is only true if the abomination which is inside the inverted commas is a complete sentence? If that is the case, should there not be be a full stop on each side of the quotation marks?
The thing is that saying 'Michael and I' (for example) is drummed into us as kids: when we say 'Me and Michael are going...' Mum corrects us with 'Michael and I are going'. So a) putting the other person first, and b) saying I instead of me starts to come naturally.
The bloke was speaking live, presumably, his little brain frantically thinking of the next thing to say, and he cocked up on this one. I'm sure, if he'd had time to think about it/write it, he would know 'and me' was correct.
I happened to be feeding ds3 when the Prime Minister's speech was live on TV. He had a big section trumpeting the Tories' ethos and achievements, including: "Let me tell you something about Michael Gove and I."