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I could be wrong, but I think there is some static electricity involved. This occurs when cling film encounters friction with another object. Electrons may move from one substance to the other, typically leaving the cling film negatively charged, then the film becomes attracted to the other object because they have opposite electrical charges. The other reason that cling film seems to be 'sticky' is because of the molecules that it is made from. If I remember correctly, it contains a large amount of polythene. This is a very long type of molecule made up of a chain of tiny ethene molecules (hundreds of thousands of them) and it is coiled and kinked around like a spring. When it is pulled it stretches - again like a spring - and when it is released it attempts to revert to its curled shape, but will never fully recoil. This is why cling film becomes useless after it has been used once.
Static electricity (which is why it attracts to itself, squirrel, even before it's stretched - yes i agree that the stretching causes a chemical reaction) - this explains why it doesn't grip very well to earthed items (metal pans etc). Your friend is correct i'm afraid paulobrad - try getting it to stick to a radiator.