Can someone explain the thin blue wire that comes off the alternator and goes to the positive side of the battery. I don't know if someone rigged this thing up. I am going to replace the alternator but want to make sure I have the right one with the right wires. It is a 2003 SXT. Thanks

 

I don't recall there being a "thin blue wire" on the alternator. Sounds like a "remote" wire for a stereo that someone hooked up in the way wrong spot. I'd disconnect it. No power wire should be going directly from the alternator to the battery w/o the correct in-line fuse or correct gauge wire, which would be something like at least 4g wire with an...~80A fuse is it?

 

I checked the area again today. The alternator has three positions at which wires are attached. The first is the battery wire to a post. The second I believe is a black and green wire in a loom to a connector. and the third is a thin blue wire under a terminal at the bottom back of the alternator. This wire does not go to the positive side of the battery as first described, but it goes to the negative side. Maybe this was not the correct alternator for this car.Or it was not grounded so someone ran a seperate wire. I see yellow number in ink which indicates it came from a salvage yard. Would all alternators be the same for neons thru out the production years?

 

For all 2000-2005 2.0L, yes; the alternators are all be the same.

According to the wiring diagram, there is a black, a dark green and a black/gray wire coming off of the "generator."
The black/gray goes to the starter motor. The dark green goes to the PCM. The black is a ground that connects to other grounds, none of which I see going to the battery.

If it is not an ~80A fused wire, which a "thin" wire is definitely not strong enough anyways, I'd disconnect it. You run the risk of fire or possible short-circuiting.