Martin Logan electrostatic speakers, How do you know if the panels are good?

I own Quad 2905's and I had to make repairs. Other than listening to them to see if they sizzle, pop or sound distorted in general, you'll have to take them apart. Two main things to consider are burns in the material or board separations from broken glue joints.

Use your ears, use good common sense, go forward confidently.
What else can you do?

In the older ML panels, keep the volume moderately low, hold your ear close to the panel and listen to the entire panel top to bottom. In a healthy panel the sound volume should be consistent throughout the panel, especially from one grid to the next lower grid on the panel.
In the MLs, you could hear popping sound only when the panel is extremely dirty or dusty and needs a good cleaning. If the speakers are kept out of direct sun, high humidity, and cleaned/vacuumed regularly, the panels could last 20+ years without a problem.