Scotch Window Film Mounting Tape will not harm molding. Tapes are made especially for use with 3M Window Insulator Kits.
3M Window Film Mounting Tape - 13.8 yard pack
FonsBleaudy Insulating Film Window Kit to Keep Cold Out Window Shrink Film Insulator Kit (5 Windows)
3M Indoor Window Insulator For 5 3x5 Windows Film Kit
3M Outdoor Insulation Film Mounting Tape, Clear Sealing Tape for Windows and Door Insulating Film, 1/2 in. x 13.8 yd. Roll - Outdoor Window Insulator Film
Frost King E/O Indoor Window Insulation Kit (4 per Pack) V73/4QPD2 - The Home Depot
3M 5 ft. 2 in. x 17 ft. 6 in. Indoor Window Insulator Kit 2141-EP - The Home Depot
7000136628, 3M Scotch-Weld PUR Adhesive TE040, Off-White, 5 Gallon Drum (36 lb), 1 Each/Drum, Aircraft products, na
Window Insulation Kit for 10 Windows of 3' x 5' - Indoor Window Plastic for Winterizing, Tear Resistant Transparent Shrink Window Cover with Double-Side Tape, 63 × 433 in
3M Outdoor Window Insulator Kit, Clear Film, Clear Mounting Tape, Fits Two 3' x 5' Windows
3M 62 in. x 84 in. Clear Plastic Indoor Window Kit 2120-EP - The Home Depot
3M UHMW Film Tape 5421, Transparent, 6 in x 18 yd, 6.7 mil, 2 Rolls percase