from time to time:

Some (but not all) 1950's infinite switches have the pilot light tapped to L₁. Others, to L2. This, obviously, can lead to unpleasantness.

I encountered this one a little over a decade ago when we were rewiring our 1953/4 Westinghouse Rainbow stove and had to replace an infinite switch (the Super Corox, of course, what else?). 

Always do continuity tests to be sure. 'Cause, if it's Westinghouse you can not be sure.

Otherwise, infinite controls are grouped in power ranges - some have '1500' Watts stamped on them or '2000/2500' or such information. Others, you have to look it up in the catalog. If you get it wrong, the heat anticipation will be off.