Oops, forgot something:
It is a common misconception that Punctuated Equilibrium is intended to explain "huge gaps" in the fossil record. Actually, it covers large periods of stasis in the fossil record: periods where there are plenty of fossils showing not a lot happening for a long time, then a period of relatively sudden change (still over hundreds of generations though). The gaps that exist are entirely explicable by the unlikelihood of creatures becoming fossils.
For example, one school of thought is that the mutations do not occur continuously but coincide with some cataclysmic event. These events could explain why there are so many big jumps in the fossil records.
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