After the last maintenance (where I also found loose parts) I also finally hooked up the projector to our HTPC via HDMI instead of VGA. However, I then noticed, that at the left edge of every white pixel on dark background, there is a red shadow, and on the right side there is a blue shadow. As if the red, green and blue LCDs weren't aligned properly. I have added some pictures to show what I mean:
It's not noticable from more than 1 or 2 meters away. In the past I always attributed this to signal run-length differences in the ~18m VGA cable, but that's not the cause now.