It seems that the solution was, in fact, cleaning the DVD . After that, ImgBurn was able to read the whole disc. As this DVD never played well on my DVD Player (it "stucks" frequently), I always assumed that there were errors on the disc (although I am aware that my DVD player is not exactly top quality...). Anyway, thank you all for the suggestions, which are certainly useful.
I have this non-commercial video DVD with a few errors. When I try to create an ISO image, I get a message like the following: I/O Error! [...] Interpretation: Unrecovered Read Error If tell ImgBurn to ignore these errors, will the resulting ISO image be a valid one? If I burn that image into a blank DVD, should I be able to play the movie on a common DVD Player?