What are some things a newbie should look for after the install of his audio? what questions should be asked or discussed?
It depends on what exactly they did to it.
New Amplifier? Make sure your fader/balance still works, that the fuses that went in the power cable(s) from the battery are the correct amperage, observe the brands they used during the install, if any of the wires are visible in the car. Make sure the amplifier's light turns off when you walk away from the car. Did they throw in a low farad capacitor and charge you for it? It'll probably have a voltage display on it if it's a piece of junk.
Sound deadening? Does your door shutting sound different with the window up? Do a frequency sweep, is there still a lot of resonance rattling they didn't address?
New Subwoofers? At high listening volumes does it sound like it's clipping or bottoming out?
New radio? Pull it out of the dash and make sure they used heatshrink or high quality crimps to connect the wires and take a photo to send to us. Is your car's original plug still there? It'd better be. Did anything they do permanently modify your vehicle? That's the primary sign of a bad installer, permanently modifying a vehicle's electric, particularly with shitty crimps, twisted together wires instead of solder, or big wraps of electrical tape where they could have used heatshrink instead.
Take photos and share them if you're concerned.