Right now I'm tearing my hear out trying to get jumping to work correctly. Originally you jumped by pressing shift + keypad key. This doesn't work with the GOG version though.

I've noticed that the arrow keys cause jumping, but that's a weak substitute. I still can't jump diagonally, and having to move your controlling hand between keypad and arrows is inconvenient.

Does anyone have an idea why shift+keypad doesn't work as intended on this version? I can't find a solution.

Maybe one could use the key mapping feature of DOSBox to repair jumping, but oh god, I just don't understand that cryptic piece of junk GUI. Maybe greater minds than me could figure this out?

By the way this has been talked about both here and with support... I'm more or less sure this was never meant to work, it's not a bug in the GOG version, it's a bug in the original floppy version too.

Yes, I was wrong in the original post. This is not a bug linked to the GOG version of the game.
I managed to reinstall the version of the game I already had, and the problem was exactly the same.

The problem is, since I last played this game, I bought a new keyboard. Covert Action worked perfectly with my old PS/2 keyboard. My new keyboard is a USB keyboard, and that's probably the source of the jumping problem.

I don't see why a USB keyboard would affect key mapping. Really, I doubt that is the problem. I don't have a PS/2 keyboard on me though, so I can't be sure.