I think if you know even a little about how music is structured the process of remembering tunes becomes easier. If all you're doing is remembering to move your fingers to certain frets at certain times, it's going to take a lot longer that if you're remembering the chord that underlies the moment and how that chord fits into the whole progression. If you can remember that kind of thing, then the details will fall into place more easily and can even change slightly without ruining everything.
It's a bit like memorizing the way to friend's house in a big city: if you know that (for example) it's on the south side of town, across the river, and that you take highway 1 before you take exit 33, and then turn left at the second junction, then to the top of the hill etc. ... that's a lot easier than thinking "I turn right when I leave my driveway, then first left, then third right, then second left, then fifteenth right, then third spoke at the traffic circle, bear left at the Y junction, then left at the traffic lights, then the seventh exit off the highway etc.
The first way of remembering allows for mistakes to be made and corrected easily; the second will leave you stranded if you make one wrong turn. That's when the dreaded "oops, made a mistake ... I'll need to start over again" syndrome comes in.
Knowing a bit about the key, which chords are likely to come into play etc., is a good place to start.
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