That's a good question. With a straight, (non swept), wing the Mcrit number can be increased by reducing the thickness of the airfoil. The velocity of airflow over the wing at any given TAS will be slower for a thinner wing than a thicker wing (assuming a positive camber wing). So a thinner wing will have a higher Mcrit than a thicker wing.
The problem is that a wing can only be made so thin before it is no longer structurally sound so the idea of sweeping the wing came about. When a wing is swept back the chord line of the wing is no longer perpendicular to the relative wind. The result is that the airflow is split into two components: 1) Spanwise Flow, which travels parallel to the leading edge of the wing, is not accelerated over the wing at all, and produces no lift.
2) Chordwise Flow, flows parallel to the chord of the wing and is the only flow which produces lift.
Since the wind is split into these two components, the more the wing is swept back the more Spanwise (bad) flow, and less Chordwise (good) flow you get.
Ex: A sweep angle of 37 degrees produces a chordwise flow that has 80 percent of the free-stream speed; at 45 degrees of sweep, it's 71 percent. Therefore the aircraft can move through the air at a higher TAS before reaching its Critcal Mach number.
Last two points: First, the more the wing is swept the less lift is produced for any given TAS, which results in poor slow speed handling. Think of all the crap on the front and back of a 727 wing. Second, fuselage components such as the canopy can now have a lower critcal mach number than the wing. Remember that Mcrit is for the entire airframe and not just the wing.
Sorry for the long, drawn out explanation, but hope it helps.