Sorry guys, I was away doing my own stuff. Forgot to check the forum. Anyway.... Here's the full story.
The game was just fine up until the first boss (Klompa). After you defeat it, there should be 2 cut-scenes. The 1st is pre-rendered, after that there should be scripted a cut-scene (turning into Dark Prince), but instead there was Prince falling into nothingness. I restarted the game, defeated the boss again... same thing. Then I loaded the previous savegame, This time something more interesting happened:
This is a life upgrade section. Well, that time, the whole section behind the door frame was not loaded, just the giant stretched skybox. If I walked there Prince would fall through the floor. (Savegame: The Lower City Rooftops)
The second time I had 2 problems. When I first got here, everything was fine. But then I died, and after loading the save game...
Everything to the right of the green line was not loaded, again just the skybox and the rest of the river (Savegame: The City Gardens). This time I tried restarting the game a few times until it loaded fine (no particular reason). Then I got to the Stone Guardian. And here's the second problem, when you die here, the game loads from a checkpoint right before the Stone Guardian encounter, the Sand Credits crate cannot be broken, and when you're about to ride the Guardian, the game crashes to desktop.
None of this happens with GOG exe, which I, btw, used to make the screenshots, the new exe just crashes to desktop when I press PrtScr.
Savegames