Incomplete files.
 

Where do I go to set it so that LimeWire doesn't automatically save incomplete files?

Thanks.

Can not be done. All p2p programs use some kind of incomplete folder. LW's incomplete folder is always found at the same level in the directory as the download folder. If you find it annoying, then perhaps change the location of your download folder. ;)
And whatever you do, don't choose your desktop or program folder as your download location. You will be risking your computer with damage if you do. You can simply use a shortcut to reach your download folder. Else: For fast & easy access, go to your LW Library window, select Saved Files folder & press the Explore button. Sample image here: Using Library Explore button to access downld folder (click on link) & the folder will open up for you.