A few problems I have had with mine (although I would encourage you not to be put off by the reputation some alfas have, I love my car but it drives me up the wall!!)
1. Check the exhaust fully, if you can get underneath it I would recommend doing so, I bought mine (2003 model) and noticed the exhaust was a little rusty but did not let this consern me, this later resulted in me having to have a whole new exhaust fitted, which believe me with an alfa is not cheap!! It wouldnt have stopped me buying the car, I would have just made sure I got some more money off!!
2. Check for any warning lights that come one, I am currently having intermittent warning lights, which I am trying to get to the bottom of, but apparently sensor faults can be quite common.
3. Wind your windows down and have a good listen both under breaking and on the throttle, whe i bought mine it began squeeling while accelarating, but not while breaking, luckly I was under warranty, but it took 3 break pad and disk changes to solve the problem!
4. if there are 2 key fobs check both work, my ar once locked me out, not a major problem as you can open manually and as soon as you turn the key the alarm stops, after doing this my key fob reset itself and i havent had a problem since!
I hope you enjoy your test drive and that some of these points are helpful, I wish I had had the foresight to do what you have done, however, even if someone had given me a big list of problems to look out for I would have still bought the car, I love mine!!