Re your Mesa, you have already identified (probably) that the problem is with the distortion channel pre-amp. I would check all the pre-amp valves, and make sure they are seated correctly.
It's often the filament pins that make a poor electrical contact due to the high current draw.
If this doesn't cure the problem you may have a problem with the switching or a dry joint on the board, which will mean a trip to a tech. By the way these type of problems can be a real pain to find, especially in complicated circuit like the Mesa.
Regarding impedance, there have been several posts on this. To summerize:
With a valve out stage full power is achieved when the speaker load is matched to the correct impedance, ie use an 8 ohm cab connected to the 8 ohm output.
Using too high a load can and does cause damage to output transformers (OT) due to high voltage spikes puncturing inter layer insulation in the OT. This spiking occurs when the amp is driven into hard clipping., ie being thrashed.
Using too low a load causes plate dissipation in the valve to increase, which can wear you valves quicker. Potentially you can damage your OT due to higher AC current, however I've not seen this (yet!).
In an amp with a well specified OT you can get away with a certain degree of mismatch. I can't comment on the quality of the OT in your amp as I haven't seen it.
For what its worth, I prefer the sound of an amp matched to the correct load.
You have a cab with 2 8 ohm speakers in it. These cab be wired in series to give 16 ohms, or parallel to give 4 ohms. In "stereo" you can connect to the two individual speakers hence two 8 ohm inputs.
If you wanted to match your amp to a 2 x 12 cab, you would need two 16 ohm speakers wired in parallel (or 2 4 ohm in series).
Hope that makes sense.