Cruise Mach Number less or more than Critical Mach Number
The critical Mach number $M_{crit}$ is defined as the lowest Mach number at which the airflow over some point over the airfoil reaches supersonic speed, that is, Mach 1. Usually, flying greater than $M_{crit}$ will produce a normal shockwave perpendicular to the flow, at the point of minimum pressure on the airfoil. I must note that if flying slightly above $M_{crit}$, there is a possibility of the isentropic recompression of the fluid, which means that no shockwave will be formed and thus no losses in form of the entropy will occur. This is especially the case with supercritical airfoils flying slightly above $M_{crit}$.

Critical Mach number for a typical transonic airliner is not equal to divergence Mach number $M_{dd}$. In fact, many aircraft will exceed $M_{crit}$ during the cruise, which you can see on the following video: 
                
            . I believe that the average value of $M_{crit}$ is around $0.78$ for today's airliners like A320 or B737.

Exceeding $M_{crit}$ does not mean the aircraft reached $M_{dd}$ or is about to lose control. Control difficulties may be possible if $M_{mo}$ is exceeded.

For A320 and B737, the maximum operating Mach number $M_{mo}$ is $0.82$. This is primarily due to the buffet (and ultimately high-speed stall/shock stall) and (or) flutter occurrence. Exceeding normal speed range may cause flutter to appear. It also may put the aircraft in grave danger if shock stall occurs. Shock stall will occur if the shockwave formed on the airfoil is too powerful and separates the boundary layer. In this case, the airfoil pressure distribution changes and introduces an intensive nose-down pitching moment. To avoid such scenarios, the aircraft are limited with Mach number as well. There might be some corrections on the $M_{mo}$ from the divergence Mach number standpoint, but $M_{dd}$ is not the primary reason why such aircraft are limited with respect to Mach number.