Firstly, a note from reader Harsh on a technique for removing sharpie or texta marks from mirrors, whiteboards and metallic surfaces:
Whenever I use a sharpie on a mirror or metal surface and need to take it off, I use any old cologne, spray the marked area and wipe it with a piece of cloth. That should do the trick. Doesn't work on paper though!
Secondly, I'd like to give a big thumbs up to reader ZXY's suggestion of nail polish remover to remove sticky residue. I needed to get the remains of a sticker off the bottom of an IKEA Riklig teapot. and a splash of nail polish remover combined with a plastic household scourer did the job perfectly. Thanks Harsh and ZXY!