This may be related to FOV or X/Y axis issues, but it doesn't sound exactly like what's described for these problems. When I start the game, everything seems fine. Once I start to look around with the mouse, it's just like any other PC shooter for about 1 second. Then, suddenly it feels as though the character's head is on a very loose swivel (this is with the sensitivity turned all the way down). It requires constant movement of the mouse to keep the looking in one direction. To explain it more precisely- in other games, I could move the mouse to look straight ahead, let go and then just use the keyboard to move forward (until I want to look or move in a different direction). With SS2, I have to constantly move the mouse to keep my 'eyes' pointed forward. If I let go, he just seems to swivel in the direction I last moved the mouse.

Any ideas what's wrong? I've tried with just a vanilla GOG SS2 install on the lowest resolution on a 23" widescreen monitor.

Hm, are you saying that crosshair is moving somewhere on it's own? Thats usually a problem if you have joysticks, gamepads or steering wheels connected while playing an older game. If you do have anything of the mentioned connected, disconnect them.

If you're talking about view bob (head motion while walking), then thats normal. It just simulates the walking. Otherwise you'd be gliding around.

If you can, please make a video recording of it, so we can easier understand what you mean exactly. Use FRAPS or MSI Afterburner for this task. I think they should work even in such old game.