At 20 000 km there's a problem with gearbox oil leak. The problem was never fixed at 100%. But there's no danger because there's no oil beneath the car. I changed drive shaft seal, but the little leaking don't want stop.
I thing that the gearbox is not "strong" enough for sporty use. And the lever don't go smooth like the first day when I change fast. Maybe lever-gearbox connection need to be fixed.
The seats, not so good. Nice supporting, but bad inner materials. Maybe the problem is in the drivers weight...
The clutch pedal makes at time to time squelchy plastic noise. It's annoying.
The engine. Very little oil leak at valve-roof from the first days, not dangerous, but also not nice.
At 40 000 km came the major problem. It was and still is, that at idle the rpm go little fancy, under the min. and back. And now, at 70% of stopping in traffic, the engine turn it off. Very nice. The mechanic say to me that the problem is the error in central computer and because of that the air presure sensor at intake manifold get fault, also then the lambda sensor don't work well even if is OK. I need to fit new software in the central unit (100-150) and buy new pressure sensor (120). They say at service: serial error on 16V engines. That's OK, but FIAT did not make recall, well, that's not OK.
Position bulb have a contact problem some times, but it's OK after few seconds.
The doors are to heavy so I need to adjust them at time to time. Annoying. Also, I was having a experience of tightening several of "forgotten" screws on plastic cover in wheel bay. And the window was hitting the door, the one screw was "get away" somewhere :) ) ) ) ) so I put the new one. Also typical Italian errors in manufacturing.
The suspension geometry needs to be adjust at 40000 km. There's a little negative angle at front tires. That's normal for Punto. It handles better :)
The headlights have a condensation problem, but that's a very rear case on my car.
A yeah, the wiper-blades, they are crap, and the levers (in the motor bay) also. There's a little ball where 2 levers get connected an this ball get destroyed, so if you want a smooth work of wiper-blades at 1. slow speed you need to buy a new electro-engine because it's all the one part. And it cost just 120.
Strange, but I have no problems with H7 bulbs, maybe because I don't turn the engine if the lights are working.