What could have caused a partial-panel service interruption when my dryer was started?
I think what you are trying to say is that you momentarily lost a phase. By the way there are 2 phases in you panel usually labeled A &amp; B. Each one will read 120V to the neutral (ground) and 240V when measured phase to phase. 

The momentary loss just might be a power company failure, but you might also be losing a phase in the panel. It might be just a loose conductor feeding from the meter to your panel or you might have a lose connection where the main id attached to your bus or your dryer breaker may not be making good contact with either its conductors or bus. Or like you said you may have a main going bad but that would be the most unlikely situation. 

Open your panel and look for any discoloration or burned insulation around the breakers. When the dryer is running feel its breaker and the main and see if they feel warmer than the other breakers. If you have one check them out with an infrared thermometer. If you have a voltage meter you can test across the breakers and see what kind of voltage drop you are reading. It should be around .05 to .03 volts. If its reading somewhere around .1 to .3 volts you are reading a higher resistance in the breaker than usual and may be damaged. Also check the conductor landings on all breakers including the main beaker and make sure they are tight. There will be a lug torque chart on the panel door if it hasn't fallen off. If it's missing you can go on Sq D's website and they will have a lug torque chart. 

I am surprised that if your utility company came out they didn't mention whether they had a phase loss or not since they should get an alarm and record if that happened. If you think this is testing is a little over the top;

This is the end result of what might happen.

So good luck and stay safe.