I have created a huge cave for my mod. It looks fine in the CK. However, when I enter the cave in-game, some of the objects (large ones) have been moved to the wrong location..

Here are two pictures showing the difference between in-game and CK:

http://i48.tinypic.com/2ihrpxe.jpg -- CK View
http://i48.tinypic.com/2tyms.jpg -- In-Game view

I have several IDENTICAL objects placed in the SAME interior cell, and they are scaled to the SAME size. I just copied them with CTRL-D

Any ideas on why this is happening? And how to avoid it? I've been having this problem with many mods and it's really annoying.

Perhaps you're exceeding the havok limit? A cell cannot exceed... I think it's +/-32,000 units in any direction. So if your cave is TOO big, and you go over that limit it moves pieces into the middle and things get weird. You may want to make that place an exterior worldspace, as Bethesda did for all of their large cave interiors.