Hi Tony,
I am new as well but have been fooling around with Limewire for maybe two months.
I had that trouble a few times, I am still in OS 10.1.5 or so I am not sure that matters.
which version of Limewire?
That might matter.
I tried moving some of them to the player area and double clicking which made them pop up in iTunes.
Sometimes.
I have sometimes found them over in the incomplete file and succesfully moved them, I generally click the end of the player bar in my iTunes window to see if they were complete or not.

Did it turn green?
Those I had the most trouble with. I think I lost 15-20 and had to start over but I have now downloaded close to 1100 songs into my player, I just keep trying.
I have played around with preferences and totally no idea what didn't work.
also I try to load (by double clicking) off the search page where it says complete.
I load most of mine from there.
Sorry I could not be more help.

Lucky dog with the flat screen.
I am just a iMac 600something 40G med fast Mac lover. LOL!