For a country like Norway, with so much wealth and such a high standard of living, it has to be said that the quality of fresh fruit and vegetables in supermarkets is often poor and sometimes appalling.
For the best produce, try visiting the open air market in central Stavanger by the harbour (Vågen). You may not get the same variety as in a supermarket but the quality is generally superior.
The fish market in Stavanger is extremely small compared say to the fish market in Bergen. There used to be four merchants selling fish but at the time of this update (Sep 2011) there are now only two as far as I can see. As well as being very expensive, there is not a great selection of seafood. In fact, some of the bigger supermarkets have a better selection of fish in my opinion. One of the things I used to like doing was to buy a bag of prawns (shrimp) and eating them while sitting by the harbour but the prices the last time I went there were exorbitant. At one time, I would have recommended a visit but not any longer.