my last question for everyone is: For PICs that have multiple Vss and Vdd's, do they all need to be connected (they are on this board), or are they connected internally?
All Vss's must be connected together outside of the chip, same with Vdd.

And nice job on the PCB...really. The only things I was going to mention...mister_e already covered them...

As far as overheating, with the PIC out of the socket and power disconnected, if you put a meter between any Vss and Vdd, what do you get for a resistance reading? How about a Vf reading (normally seen as a continuity test on a meter when really it measures a diode's forward voltage)... Now try it with the PIC in the socket and power still disconnected?
Then hook up the meter to Vdd & Vss, turn it on volts, put the PIC in the socket, and plug in power just long enough to read the meter. Did the meter come up to system voltage? In other words...dead short somewhere on the board?