It's always nice when a PO decides to replace the original spare with a tire which doesn't quite fit the car! I guess that's what I get for being smart and moving the spare to the front so I could keep two studded snow tires on the rear allowing me to get to work even after a little snow. Anyway, turns out that the offset on my spare is about 20 mm more than on the snow tires, and this caused the tire to rub against the suspension when mounted up front. It took me a while to figure it out since the symptom was steering wheel shake at very low speeds (20 mph), but which went away completely when speeding up. Didn't make any sense.
Now I've mounted one of my summer tires on the front instead. Shouldn't have any more problems, and the wheel looks much nicer too... :-)
Ulf