The expression is encountered in legal field with this approximate meaning: a clause which is broad and vague enough to extend obligations to unspecified ones.
I read that the expression comes from "to sweep in", but can't really grab the meaning of "sweep in" in this context.
This page explains the use of a sweep clause.
Best Answer
In the fashion that it is used in the terms Sweep Clause or Sweeping Clause it implies that the clause will "sweep in" or "collect" any items that may have otherwise been missed; ergo the sweeping clause is "a clause wide in range or effect that collects what might otherwise be missed."
Thanks to Dan Bron, we also have the origin: it came from the act of sweeping as with a broom, which grew into the "to collect by sweeping" definition which is also now used in games and contests to denote an overwhelming or complete victory (such as when you hear an announcer claim that an athlete has "swept the board"). See here and here for Dan Bron's references.
It is important to note, however, that the term Sweep Clause in and of itself isn't anything more than a description for a type of clause (such as Noninterference, Jurisdiction, Severability, etc.). It is the legal language contained within the clause that give it the power to "catch items that may have fallen through the cracks," not its name.