I think Michael is right, at low speeds the alternator is not supplying as much of a charge back to the battery, I am pretty sure when you are idling at or below 800 RPM'* the car starts to pull more from the battery, which sounds like what you are seeing.
I have always had my lights dim a little bit when braking, and when rolling a window up or down.
The only possible way I can think of to try to solve this is to upgrade the big 3 wires, and then maybe upgrade the alternator, clean the grounds while at it like Jusin suggested.
Here is a thread where Art did his wiring, and got the alternator upgraded.
Alternator-High Output at idle Please!
Getting an AGM battery may help a bit also, forgot about that.