I changed the thermostat, and had the radiator checked for exhaust gases at the Subaru dealer. The dealer told me that I don't have a blown head gasket.
For now everything seems to be working properly, haven't had to add any coolant for a few days, but the car hasn't been driven for more than 20 miles at a time. Later in the week the car goes our 80 miles or so, so I'll see what happens then.
I have the impression that it can be really difficult to get all of the air out of the system. I noticed, when looking at pressure testing equipment there are special tools to make sure you get all of the air out of the cooling system when refilling it. Funny, I never had these kinds of problems before, and I pulled the engine our of our 81 subaru a couple of times.