I have indeed had some pound coins which were tatty round the edges and had to be pushed through a self-service checkout several times or wouldn't even go through at all. I still hadn't realised they might be fake, though.
I have noticed that a lot of old 10p coins are noticeably a lot thinner (presumably worn down rather than starting out thinner) than new ones. Is this as it should be or should I start looking at these with suspicion too?