Just checked in to "Handling the Big Jets" index, and found a list of references to Mach effects. On looking up a selection I find that they cover all the various things that happen as you move higher up the transonic range. These are:
Increasing drag.
Variations in lift, whch produce -
Lateral instability and roll control problems.
The rearward shift of the centre of pressure in the high transonic range, which produces -
A nose down change of trim and -
An increase in longitudinal stability.
Transport aircraft, except Concorde, are not designed for supersonic flight, but are designed to get as high up the transonic range before these effects begin to kick in. The first uk jet I flew would not go over .78, even straight down, but most modern transports fly quite comfortably in the .9s.
Dick W