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At my undergraduate institution if you look at transcript key, it says W=non computed and the Ws I have, have never been factored in my gpa.

I looked on LSAC website, and when I typed in my Institution, it said Ws were omitted from my school and when I called the LSAC, the representative asked if my transcript was on file, and I said not yet, and she said OK whats the name of your school and I told her and she told me Ws were omitted from my school.

Other than those things, how much should I be worried that when I submit my transcript they;ll mess up and count them as punitive?

How about not worrying at all unless and until they actually mess up? If they mess up, you can get them to fix it. You really ought to relax about this a bit.