It can mean “a few times”, but you’re right that there is some ambiguity (though less in the passé than in the présent).

Some other options are plusieurs fois, à quelques/plusieurs reprises (same quantifier but with this noun no confusion is possible), en quelques occasions (same deal) …

That sentence doesn’t quite feel right, although it is probably grammatically correct. That quelque fois at the end of the sentence is probably what doesn’t work for me. I would say:

J’ai regardé ce film plusieurs fois.

Note that plusieurs could be as few as 2 or 3 times. It does not necessarily imply many times.

Probably only in familiar spoken language, for more than 2 or 3 times, you could say:

J’ai vu ce film plein de fois.

For only 2 or 3 times, you could also simply say:

J’ai vu ce film deux ou trois fois.