The first obvious problem was that there was some rust at the rear wheel arches. (Virtually every other 480 I have looked at has also had this problem.)
One of the "day-glow" bulbs needed replacing and has continued to short out ever since.
The tailgate leaked despite it's elegant "rimless" glass. This was in part due to the tail light casements being cracked, allowing the water run-off to enter inside the car. I ended up neatly fiberglassing them to the body... which helped a lot and looked great... but somehow water still was getting inside! Again, loads of 480 seemed to have these cracked casements.
One of the hydrolic arms for the tailgate repeatedly poped out of it's housing whenever I opened the back until it finally stopped with no apparent reason.
The information display actually worked!...but the speedo did not so I always had to gauge my speed by other means.
I had to have the entire exhaust system replaced at different stages of ownership and a new cat-box fitted.
As my car was a limited edition, it had the half-leather seats, but the driver's seat was suffering some wear in the place where the seat belt gets crushed between you and it whenever you get out. (The arm that holds the belt for you to grab was broken like some others I've seen and exacerbated this.)
A seal between the cylinder heads and the ignition system failed, allowing oil to prevent proper engine firing frequently.
Finally, the gearbox began to have problems, making an eerie whirring sound and leaving me wincing each time I put my foot down as to what what might happen as a result. I realised as a 12 year old car, it could not have more money poured into it.