Renegade electrical issues.

I recently purchased a 2002 liberty renegade. 2 days later the jeep wouldn't start. jumped it, started, but ran very poorly (rough). Dealership said it was just the battery, and replaced it for free. but, said it was running poorly b/c the vehicles computer had to be reset. Never heard of needing to reset a computer after changing the battery. Is this true or am I being fed a line.
My wife also says that after truning off car and opening door, tachometer jumps. Is this normal (a safety feature maybe?), or should I be concerned with this vehicles electrical problems?

I've got all kinds of electrical glitches in my 02 Lib...The dash lights brighten and dim as I drive at night. The FM radio works fine, there's nothing fine about the AM (oh well), but the CD player sounds like Beelzebub and his minions have taken up residence in there...doesn't matter what's playing. I cleaned it to no avail. Currently waiting on the AC fan switch to go out as it has on my sister-in-law and my niece (as they both also have 02 Lib's, too).

While driving home from visiting daughter in college, we passed a car carrier hauling some vehicles, one of which was a Lib. As we were about to pass it, it's headlights came on for about 4 seconds and then went off. My wife who was driving didn't say anything, so I cautiously asked if she had seen that. She slowly exhaled and said she was glad she wasn't seeing things. It was then that we decided that most Jeep Liberty's are possessed!!