Interesting question because modern cards are generally sold in pristine condition and they are immediately placed in the most protective storage, the very idea of card restoration is foreign to today's card collectors. To be honest, apart from the removal of gum stains, the methods people have used in an effort to restore value or increase the grading have done more harm than good.
By that I mean, repaired cards are rated by graders in the lowest grades and are better off left in the original condition. A pin hole will lower the grade, but if you try to fill in the pin hole it will cost you more. Black edge chipping will lower the grade, but if you use a black marker to try to disguise the chipping it will cost you more. If you try to shore up soft corners with glue it will cost you more than the original grade deduction. If you sell a repaired card without disclosing it, expect to get it back.
As far as I know there is no way to get out a water stain that has gone through the layers. Smoke damage will linger and mildew, well I'm not sure I ever saw a moldy card, but I wouldn't want it if I did.

I don't know how you are removing gum stains, but rubbing hard with a nylon stocking does well for the front picture. That will take away the sugar buildup and the underlying card is usually fine. However if the gum stains are on the back of the card, they have usually seeped into the cardboard and can not be fully rubbed out.
The removal of gum stains is the only bit of card restoration I would suggest anyone try and of course that would be mainly on old cards. Only the Indiana Jones of recent memory had gum and it was in plastic. Any other repair or restoration to hide damage will result in the card grading being nullified. Only a very expensive, probably very old card, holds any sort of demand/value if it has been repaired.