Alright, here is the PCB layout.
C1 is 4700uF Electrolytic Capacitor
C2 is a 0.1 uF ceramic capacitor
C3 is a 10uF tantalum capacitor
C4 is a 1uF tantalum capacitor
C5 is a 100uF electrolytic capacitor
VR1 is a 7805
VR2 is an LM317T (with big heatsink behind it)
IC1 is the PIC
TS1 is a temperature sensor
RF1 is a 2.5 V precision voltage reference
Vo is a 10K potentiometer, for adjusting the LCD contrast.
The external potentiometer (connected at POT and REF) is 5K
R1 is 240 ohm. It is also not located at the spot on the PCB anymore. I took it out of their and drilled new holes closer to the voltage regulator, after reading the part in the data sheet over load regulation. While I originally thought it fixed the problem, it came back later. Perhaps the connection just got worse? Does anyone see anything else wrong?