1. Driving lots of LED displays directly off of the PIC too much current.
2. The buttons are connected to the display. I take it the intention was to also multiplex the buttons with the display by reading it periodically, but if you hold the buttons down it will connect the pins directly to ground either turning on or off the corresponding segments of the display and also possibly sinking lots of current from the output pins. Should have used the unused pin RA4 (see #6).
3. As mentioned earlier, no pull up resistors on the switches.
4. MCLR connected directly to Vcc, I usually at least use a resistor between them.
5. No load caps on the crystal, probably wouldnt even start oscillating.
6. RA4 tied directly to ground, could sink too much current if the pin is incorrectly set in software.
7. No caps on Vdd near the PIC, possible dirty power.
EDIT: Strike number 5, didnt notice ceramic resonator. I've never used those personally, so I dont know if its use was correct or not.