-Every screen is off center toward the lower right corner, which makes escaping and using menus impossible. Can't be tweaked from options since the OK button is probably on the part of the screen I can't get to.
-I hit new game and it starts to load, then it just stops. I get a screen with a background and nothing else happens. I have to exit by hitting control-alt-delete.
Anyone else have these issues? And, if so, what did you do to correct them? Any advice?

I'm having the same issue as well! Come on man! I just got this game recently!

I can't get resolution larger than 1360x768!

I followed this link and got the game running in window mode.

http://www.gog.com/en/forum/ufo_series/how_to_run_ufo_as_in_windowed_mode

Then i could get it to the resolution i wanted.
After that i removed the code in the exe file that put it in window mode and now it works fine in full screen.
One thinge to note is that puting the game in widescreen gets you a smaller screen.
You need it to be in 4:3 to get the picture to cover the hole screen.