The only problem I can see you might have, and I stress 'might' is heat pooling. Most computer monitors are built on the concept of convection ventalation. ie: heat rises.
For instance, the monitor I am using now, has -zero- holes in the sides to ventilate heat, only in the top and bottom. This monitor also has some circuitboards which stand vertically along those sides. So if I were to rotate the monitor 90 degrees, the board that would now be the 'top' would be sitting in all the heat generated by the other board and powersupply as well.
While this heat will probably not cause any immediate damage, it can easily shorten the useful life of some parts. Just keep an eye on it. Judge the warmth of the monitor case for yourself, if it feels toastier than usual, you may want to stick an el-cheapo CPU fan to the monitor case. Just enough to move some air, doesnt need to blow the monitor over.
Taking the plastic shell off the monitor may not be as dangerous as you think. Many monitors, especially the larger ones have insternal metal shielding to keep you from zapping yourself (and kill rf emmisions from bleeding out the back). In my cabinet, I pulled the plastic off of the 19" monitor and gained nearly 2 inches of side to side clearance, and an inch of depth as well.