No issues with mine - 133,000 miles. New cover gasket, header tank - that's about it in terms of engine probs.
Not stunning performance, but just read all the posts about the problems with the (petrol) turbo version, and the endless posts about egr valve probs, turbo probs and particulate filter probs on those 'wonderful' diesels as they age. And of course the balance shaft problems as well.
I get about 34mpg overall, and while a little more 'umph' would be nice, it still gets me where I want to go at a decent rate. Running costs v a diesel must be broadly similar, given the difference in fuel prices.
And it's smooth, quiet and civilised. And yes, I've had diesels too. An a4 b7 which was rather nice. Although I expect it's balancer shaft / oil pump would have been amongst those that failed ----
Modern diesels are great - when they're working properly. When they're not, well, see above! When I was looking for the b6, I really wanted a 2.5 Quattro. Well, thank goodness I didn't find one of them, what with their fuel pump probs and chocolate cams. I'd lusted after a b7 2.0 diesel - and ever so relieved I couldn't afford one at the time.
All this said, the 1.9 diesel is a very nice car - and if I could have found one, I'd have bought it. The reality is that the 2.0 fsi petrol serves me very well.