I took down a shampoo dispenser and now I have several big blobs of moldy silicone caulk on the shower wall. I bought a plastic razor scraper and a bottle of Goo Gone Caulk Remover, which gets high marks for removing silicone on Amazon, but I haven't even made a dent. I think part of the problem is that the wall is vertical (duh :) and the remover is liquid, so it doesn't stay on the caulk long enough to do the job. Is there a gel formula out there that works well, or some other technique that would work better?
If you saturate toilet paper with the remover and slap it on your vertical surface it will stick there and hold it against the caulking. Practice a couple times with water to get a feel for the appropriate amount of moisture. Scrape off as much as possible before you start in with the remover though. Just to clarify, you should be using a plastic blade in the scraper so you don't damage or leave marks on the wall.
EDIT: BTW, you can also use acetone (i.e. nail polish remover) to remove silicone caulking. Acetone attacks some plastics, so I'd only go this route on tile.
EDIT 2: If neither of those options work, you can also go to an auto supply store and pick up an adhesive eraser wheel. You use these with an electric drill and they are designed to take adhesives off of auto bodies without damaging the paint. Again, this might not be the best thing to use on a plastic surround.
I had the same situation. Old shower dispenser had been attached with silicone. After pulling it off, the silicone was completely intact on the shower wall. Shower is an acrylic shower stall fitted into the wall around the tub. I found a bread knife in the knife drawer, about 10" long, non-serrated (not the sharpest knife in the drawer). Holding both ends of that knife, sharp side down, thumbs providing a little bend in the middle, I found that I could slice that silicone almost down to the wall. A few precise, surgical passes, scraping the wall a little bit with no damage, and it was gone in no time.