Well, 'lucille', all getting a bit esoteric now for a simple question!
99.99% of the time that 'M'crit' is 'used' it refers to a wing, as that is where the shock induced drag-rise is most significant (just above Mcrit) and the largest trim changes will occur.
I believe, however, that in purist terms it refers to ANY part of a moving body (including that well-known Aerodynamics student's nightmare, a 'right cylinder in supersonic flow'), and in my defence, your honour, submit
<10. The critical Mach number is precisely defined as that freestream Mach number at which sonic flow is first encountered on the surface of a body. The large drag rise due to compressibility effects normally occurs at a freestream Mach number slightly above the critical Mach number; this is called the drag-divergence Mach number. In reality, Caldwell and Fales had reached and exceeded the drag-divergence Mach number in their experiments. But their introduction of the word "critical" in conjunction with this speed was eventually the inspiration for its rise in later coining the term "critical Mach number." >
from the comprehensive NASA background document to supersonic flight by
John D. Anderson.
However, all of very little interest/relevance to the initial questioner!
<Or is it better defined as when the pilot is first aware of it's effects?> Certainly if the canopy reaches Mcrit first on a swept thin wing aircraft, the pilot may indeed notice 'buzz' on the rudder.
In pure transport operating terms, as you say, MMO is relevant, and the extra power needed to cruise above Mcrit shows on your fuel flow gauges!
Reckon 'Flamgat' will have passed out by now?
