Well the engine is bulletproof. Cambelt needs to be replaced every 5th or 4th year if its been driven in city and short journeys a lot. Personally I'd go with every 4th regardless.
The 6-speed M32 gearbox however, (that sits in the 1.6 and 1.9 diesel) are well known for failing due to weak bearings. You will first hear a whining noise in certain gears and at certain rews/speeds. Seems to be very common. Google this gearbox and you'll find plenty of info about this problem.
The gearbox might last if you're lucky but if youre not, you're looking at an expensive rebuild.
BUT I'd say its a good buy if you can get a really good price on it, has been taking care of and has full service history.
Look for one that has mostly been driven on long journeys and not city driving, as this can cause the DPF filter and EGR valve to clogg up. The DPF is suppose to last the lifetime of the car (according to Fiat) and is suppose to regenerate and clean itself. DPF stands for diesel particulate filter. From what I understand, it can become defective and clogg up due to short journeys and lack of oil changes. If that happens, you might need to replace the DPF. Apparently its an expensive job. Good idea to rev out the engine every now and then and have some fun with the car, in other words.
The same goes for if city driving is what you're planning to have the car for. Then you're better off with a petrol.
Also - definitily recommend finding one with parking sensors. The visibilty around the car is awful.
My mom has had the same car for about 2-3 years now. Except for some small niggles, It's been a good, reliable car. She's had to replace the front spring struts, the glowplugs, a few bulbs here and there. Rear badge and driver door rubber list have fallen off. The battery just recently started to drain a few times. Mechanic says its just the battery, so hopefully its not the alternator. And yes, she has the whining noise in the gearbox. During this time of year, the gears can be very stiff in the first few minutes. Especially first. I've read that the gear-linkage cable tends to rust. Fiat replaced some of them under warrenty for free, apparently. It's a 2009 model though.
There are things that annoys me though and where I think they could have done a better effort when designing the car. Cup holders are rubbish, not that much legroom in the back, heat ventilation to the legs is very poor during the winter. handling is very stable and good but the ride tends to be a bit jiddery. Other than that... nice car if you're looking for something different and stylish. It's very quite at high speeds, even more so than in a vw Golf. Fuel economy has been impressive.