For me the weirdness with the mouse occurs in windowed mode as well as fullscreen, and depends on how fast I move the mouse. When moving the mouse quickly there is little difference; but when moving the mouse very slowly the pointer will actually not move to the right or down at all. The behavior is the same when using mouse drivers instead of DOSBox's internal driver, so I suspect this is a quirk of the game's design.
I analyzed the issue awhile ago when it was reported, and learned of a way to work around it. Place the attached program in the game directory and run it instead of A10.COM, then the strange behavior should stop, but the way the game moves the mouse pointer (like it "gravitates") to certain buttons when changing screens should still work correctly. Assembly source is included in the archive.
Edit: Updated the fix program to add support for the CD version.