Dimming of Headlights and Dash Lights

I've got a 1996 Grand Prix and the headlights and the dashlights are dimming consistently. It's really more of a pulsating. I just replaced the alternator about a month ago. Some of the warning lights have been coming on at different times too. Sometimes the service engine light, sometimes the air bag light, sometimes the ABS light, sometimes the low coolant light (although this one is from a dirty sensor that I haven't taken the time to fix). I don't have a clue what would be causing it to do this. Can anyone help? Thanks