How to remove scotch tape brown residue from album covers

A light use of any typical “salad oil” can loosen and even remove - I’ve used it for decades on furniture, computer parts and labels. 
Find an area to test it. Don’t saturate, just a light application. Most remaining stuff usually just balls up and can be rubbed off. The left-over discoloration may not be removable 😞
As someone said, not all printing processes are the same, so use care. 

I repeat, though I don't know why I bother ;-) : Bestine was created specifically to dissolve rubber cement. "Scotch tape brown residue" = rubber cement. Capiche?

Hand sanitizer.  Do not rub hard.

Ideally, lacquer thinner is the best solvent for that and it will dry out very quickly not leaving a stain. You can get a quart at Home Depot. You must wear gloves and be in a well ventilated area, preferably outside. Lacquer thinner is explosive like gasoline if the concentration gets too high but, you will have passed out before that happens. 
Brake cleaning fluid might also work but I would go with the Lacquer thinner. 3M makes an adhesive remover. All it is is lacquer thinner at twice the price. 

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Bonjour 

Essayer pour enlever les traces de colle, d'utiliser de l'essence F (Détachant Textile et dégraissant Métaux)

I’ve had great success with lighter fluid. Friend of mine who deals in vintage re rods turned me onto it.

3M makes a citrus-based adhesive remover that's just the ticket.  You might try WD-40, but it leaves an oily residue.

My best success has been with a good single malt scotch......for me. 

+1 Eucalyptus oil. Smells nice too.

AG 🇦🇺

I use Eucalyptus oil first. Spread a bit over the shop label or tape with a cotton bud and do this a couple of times. Usually, it gently peals off. If not, revert to some of the other suggestions.

That bites. I used doodle some on covers and have a number of value-reduced albums.

a kneaded eraser can work wonders on cleaning up old album covers from a lot of types of debris.

Goof-Off^^^

Magic Eraser; Good-Off; Goo-Gone or lighter fluid 

The best way to remove those ugly stains is with a scissors.

IF the adhesive is crunchy, GENTLY drag a new single side razor over the top to RAKE not cut the adhesive. Don't drag the whole surface at once. Drag OFF the cover, not ON to the cover.

If it is softer,

Like the guy said, peanut butter (OIL) is a good softener. Just about any type of oil will work. Work quick, a little dab will do ya. Dip a Q-Tip in baby oil, 3 in one, or what ever you pick.  Work the spot with the Q-Tip and wipe. It's better to treat more than once than over do it and have the oil penetrate the covers ink and then into the paper product..

If you get it down to a science, then wipe the corner once or twice with a little isopropyl on a toilet tissue, ONCE or TWICE, no more..

Just so you know, what mechanics are really good at (IF they are worth a hoot) CLEANIG THINGS... 3/4 of my time was cleaning things so I could fix them...GROUT and drilling MUD.. Wonderful to clean..

I prefer Bestine---created to dissolve rubber cement---over Goo Gone. I use it to remove the glue left by the price stickers I remove from used LP covers. It doesn’t stain the cover as Goo Gone sometimes does. It's sold at art supply house (and of course on Amazon).

As for inner and outer sleeves, check out Vinyl Storage Solutions in Canada. The new standard in LP protection.

All album covers are probably not the same, but I've been successful using "Goo Gone" (available everywhere). Just don't let it sit on the paper too long!