I'm not sure what you're able to see at this point as far as residue or damage to the screen (if any). But moving forward, you'd be best to use an LCD Screen Cleaner like Monster, RCA, Dr. Clean (etc) that is specifically designed for cleaning LCD screens. Most of those packages comes with a soft microfiber cloth, and you'll want to be very gentle during the cleaning process, and spray the cleaner on the microfiber cloth, rather than the screen.
Oh Know!!! I have just cleaned my massive expensive new TV with windex wipes to try and fix all the smudging from hubbys attempt at cleaning it with spray & wipe the other day....not to mention using cheap(clean) dishclothes! I just read the back of the windex wipes and saw NOT FOR USE ON PLASMA SCREENS. I paniced and tryed wiping it all of with wet clean dishcloth then dry clean dish cloth. then i jumped on the net and found this site, reading everything ive done is WRONG! SH**,Now that ive stuffed up,what can i do to fix it? We never recieved a cloth or any instruction when purchusing the tv & had know idea