We use that plastic film you are talking about. Our place is a bit drafty - not terrible, but enough that the gas bill is high and there are noticeable temperature gradients. Plus, on the coldest days/nights, the apartment struggles to reach 68F even with the windows covered with plastic. The plastic enables the place to heat up quicker, reduces drafts, and reduces the gas bill.
We just took it off tonight as our landlord is coming round tomorrow with an estate agent to put the place up for rent as we are moving out soon. I don't feel guilty about having put it up, I just want to make sure the place looks good so we can get it rented out and not have to worry about breaking our lease. Actually, I figure if the landlord is renting a place that isn't properly insulated, then tough luck, they'll have to put up with it.
Anyway, we use masking tape to stick it to the window frames/wall as the double sided sticky stuff they supply with the kit is rubbish, it doesn't work at all. Unfortunately the masking tape does occasionally peel a bit of paint off, but we plan to touch it up when we move. The double sided sticky tape isn't much better, as it leaves a sticky residue behind.