This seems like the likely culprit to me. I had the radio volume up pretty high the other night and definitely noticed that I could see the lights dimming slightly with the beat. It was barely perceptible, but definitely should not happen with a factory stereo--and especially not the non-Bose 6 speaker stereo that is probably under 100w peak/max!
I am about to install a 200w amp, so the weak electrical system may definitely be an issue! Hopefully a new battery will improve things, as a capacitor should really not be necessary on a 4 channel amp with no subs.
Given how cheap Nissan went on the OEM speakers though, it wouldn't surprise me if the OEM battery is among the worst made. Has anyone replaced it and seen an overall improvement in the electrical system?