Did I damage critical engine electrical components when I jump started my battery?

:uhoh:I jump started a dead battery in my 2011 Ford Shelby GT500. The car ran OK for a while although a little rough but later the battery was dead again. This time I replaced the battery with a new one. Even with the new battery my engine still ran very rough and stalled a few times. Someone at the dealership told me that if I jump started the battery or replaced and installed a new battery incorrectly that I could damage electrical components. Is this true? Can you tell me exactly what electrical components can be damaged? Please help. Thank you.

OH MY GOD!!!! please tell me that this is some kind of prank or joke........You got a brand new '11 GT500 and you had to jump start it?!?!?! Well you shouldve left it where it died, called the dealer and have them pick that thing up with a flat bed (prefer a inclosed trailer from the dealer) and have them fix it because you have warranty on it....if you were worried about paying for something, I can tell you that since you touched it, you now have to pay a lot more...PLEASE "CALL" the dealer and have them pick her up and pay what ever you have to get it fixed properly.
And yes, you could have damged something when you hooked up the wires incorrectly and/or jumped it with another car/battery and had those jumper wires incorrectly placed (and no, its not connect the jumpers directly to both batterys!!)