Poor Starting - want ideas to debug

With 250,000 miles, I'd check the compression and do a leakdown test to see if things are going to get expensive. Next, I'd look to see if fuel was adequate for startup, assuming you have already verified that the ignition is OK. Since this can get involved, with an electric fuel pump, return line, regulator, fuel pump relay, etc. the details should be looked at on miata.net, usually in the garage section. Occasionally, a bad ignition switch can cause an intermittent or no start problem. You have enough time and milage for this to be a possibility. I doubt that roll starting is related to your problems.

I agree with Chuck, I don't know of any damage that can be caused by bump starting (as we've always called it).

Chris

The only potential damage is to the front bumper and whatever it strikes, if an inexperienced owner loses it when the engine fires. Or to said owner if he tries to push the car himself, trips while hopping in, and gets run over. Stupid pilot errors? Surely. But Mazda has to disclaim the concept or face lawsuits.

If bump starting breaks something mechanical, it was ready to break soon anyway. The stress isn't much more than a clumsy shift.