Is this real wood or the shiney plastic paneling? If it is real wood you should be able to use Goo-Gone, which will remove the glue from the tape. You can purchase it at any hardware store. You may have to oil all of the paneling to make it all blend. In my former home I would just pour a few jugs of lemon oil in a paint tray and use a thick nap paint roller and let it sit for a few days. Most of it was absorbed and there was vey little to wipe off. If this is plastic the Goo-Gone will change the gloss and I don't know what to do about that. Goo-Gone is a petrol based product.

I've used the product listed below to remove old silicone caulk from shower doors. It works! If the duct tape adhesive has already reacted with the finish on the floor there may not be any way to prevent damage to the finish. Spray the tape with the cleaner, let it soak overnight and then use a plastic spatula or credit card to gently pry the tape off. You may have to do more than one treatment. I believe you can find the cleaner at Home Depot or Ace stores. Here is a link that might be useful: cleaner

Sorry, I should have explained better. The tape is bubbled and really has to come off. It is obviously not mudded over the top of the tape not sure about underneath yet. I know that i have to retape, I'm really wondering about the joint compound and how to start over the paint. Do I need to prime or will it work over the old paint? The paint is probably at least 30 years old. The scoring is a good point though, i would have started pulling. Thanks again!

How about Goo Gone? I use it to remove old tape from glassware, etc. I think you could then rub it with a little extra detergent to remove any traces of the Goo Gone before you put it in the wash.