I needed to get rid of the smell from the air duct, so I have the car turned to the on position (without ignition, i.e. engine is off) and connected a battery charger to the battery, so the car won't die. The next morning, the car started fine, but the check engine light was flashing. When I drove it, I noticed it car was misfiring.

Could the charging damage anything that could lead to the misfiring?

Thanks,

 

sounds like a problem that I caused when charging my '97BMW - turned out to be a burned out diode in the alternator - have the alternator checked - the alternator is integral to electrical system, won't hurt to have it checked