The shop that looked the the wheels did take them apart which is when they determined that the hubs were worn. They re-packed them with fresh grease and tightened things up, but explained that the hubs were worn and that it would be cheaper to buy new wheels than to replace the hubs.

If it is normal for cassette to wear out after 3000 miles, then I guess I shouldn't be too surprised. I'm not terribly good at cleaning my bike, I'm afraid. It gets a clean once a month maybe. And it does have to cope with a lot of silt, salt and grit.

I will need to do something as the shifting isn't good, but I think the shifting problems are mainly due to the worn chain. But is it worth changing just the chain for now and putting off the rest for a while longer? Or am I better off just doing the whole job now as it will all need to be done soon anyway? (I realize this is somewhat retorical as you can't see the actual wear on my bike..)