Our air conditioner worked all weekend on 20 amp. Are we creating any future problems?
Provided you are using your RV's power cord (a proper thick cord) with a dogbone, I think you're fine. I assume you verified it is a 20 amp circuit and not 15. Household extension cords should not be used for a number of reasons, and damaging your air conditioner due to inadequate power is only one of them.
"You can't buy happiness, but you can buy an RV. And that is pretty close."
Just don't run any other large draw items (i.e. microwave, elec water heater) at the same time as the A/C and there shouldn't be a problem. If you have the hardwired EMS from Escape it will show you the instantaneous amps you are drawing and it will shut off power if there is a voltage below 104 (Error Code E4). I don't know exactly what the Dometic overhead A/C can tolerate, but my mini-split is ok with +/- 10% which is a low of 103.5. So the EMS will provide protection for my A/C which is the primary reason I installed it. If the Dometic doesn't like anything below 108 as I see Jon suggests then you need to be careful as the EMS won't be shutting down power early enough to prevent possible damage. I think in reality the A/C won't be damaged with short amounts of runtime between 104 and 108, otherwise there would be a lot of unhappy customers out there that had their A/C damaged during a low voltage condition in a campground when the EMS should have protected it.