Thanks a million for all your suggestions everyone! The lesson to be learnt here is of course: keep a squeegee in your shower and wipe after showering or hang shower curtains over the glass

. In our last apartment a squeegee came with the apartment which we used and probably made the difference. I don't know why we did not think of that when we moved in.
Anyway, I think that the glass was damaged by one of the previous tenants through cleaning with some harsh acids as there are cloudy areas which I think have been etched into the glass and they have been there since as long as i can remember.
I tried all the cleaning products which you have suggested and then some. What worked best was actually rinse aid from the dishwasher - it contains citric acid and 3 times the amount of active ingredient that durgol and all the other identical products contain.
Yesterday I tried one of the more weird suggestions I found on the interwebz:
It has made a difference! I was doubtful but it has helped. My method:
1. Spread WD-40 on the glass with tissue and leave for a few minutes.
2. Scrub hard with a sponge.
3. Scrub gently with fine steel wool. It does not scratch if one is gentle.
4. Clean immediately afterwards with balls of newspaper and window cleaner.
The glass is still not perfectly clean but i think it will pass inspection now. Wear and tear and all that.
Note to anyone who might try this: My shower doors have normal glass without any special coatings - I checked with the company that installed the shower. Also try it on a small section of the glass first to check that nothing strange happens.