Check the folder permissions of the folders you are having problems with.

Also check for viruses,etc. it sounds like your folder is locked or semi locked. ___ (a) Incomplete Download File won't delete at all (click on link). This link has many suggested utilities to use.
Getting access to locked files or folders: (b) How to take ownership of a file or folder in Windows XP (click link)

Make sure LW is closed when you try to move files.

This could possibly be some kind of bug in the new versions, though this is the first I've heard of this problem, could possibly report it here LimeWire Beta Forums