When I enable distant land, the starting ship just outside the Census office appears to be permanently stuck there if I am standing far enough. As I move closer to it, it'll eventually disappear.

Also, the starting ship's reflection will always appear on the water no matter how I view it... even when there's no ship on there!

How do I fix this problem?

This question should be asked in the http://www.gamesas.com/index.php?/topic/1159516-morrowind-graphics-extender-mge/ and I'm quite sure you get help there much faster than here.

Yep, that is the proper thread to use.