If it's a 1.9 then look out for gearbox noise (search the threads, I'm scaremongering because mine just failed, most are ok, but noise from the box is never good)
Some common issues are timing belt, water pump. make sure they are changed well before the service interval (Alfa say 90k for the belt, EVERYONE else says 60k, so scale that up and get it done if required)
The DPF is a constant topic of discussion and having it remapped and DPF/EGR delete is always recommended by everyone that has it done.
I'm currently following FixItSan's topic of drilling out the DPF to see how it goes (I do't want to go first on that one, so am happy to learn from his experiences)
The 1.9's run great on Biodiesel so if you can find a good supplier then £1 a litre is always better than £1.40+ a litre pump diesel (I was one of the first on that and can confirm no problems after 10k miles)
Other than that, make sure you wash and polish it as often as you can, keep the wheels clean, and don't let the kids drop crisp wrappers etc in the rear foot wells. It' won't effect the car, but every time you look at it either in a reflection or as you walk away from it you'll know.
the feeling you get as you walk across a car park and think to yourself "that's my car" is priceless.