The idea that people can move when time is stopped is not, as Chrono claims, completely illogical. Certainly, in a standard Newtonian sense, time passes at equal rates for all objects; this is the only way we can accurately measure the speed of, say, a passing car. But as Einstein realized, while the speed of light is constant, time and space are not. Indeed, they are malleable, and relative.
What this boils down to is the fact that time can be stopped for object or set of objects, referred to as a "reference frame" in relativity theory, and still moving for other objects. Hence, at least on the surface, it appears that one could "stop" time and then commit one's nefarious crimes and such.
However, this fails to consider just how one would go about stopping time according to relativity. The rule that applies in this case is that as something's speed approaches c, the rate at which time passes for it approaches zero. Therefore, one could stop time for oneself (assuming one could reach the speed of light), but that would not help in terms of screwing with people. And to stop time for another reference frame would mean sending it zipping off at the speed of light. In conclusion, it seems we will never accomplish our undying dream of cavorting in a world with no time and then watching everything fall to pieces when time resumes. But we will still bide our time, and plan.