The gate waveform is OK, but the duty-cycle is very low so it will be harder to see the LEDs on. Remember - This is a PMOS device, so it will be 'on' when the gate is low.
Now, for the drain, you can see that it's on for a short time, then decays in an RC-like manner. It's probably the RC time-constant of your scope+probe. It looks like the segment drivers are off at this time; if they were on, you would see a rapid decrease in drain voltage rather than a decay.
Check the sequence for your segment-drivers. You want those to go 'on' when the gate is driven low. And you probably want the 'on' time of your PMOS driver to be longer (gate=0v for more time).
Hopefully you have not damaged the gate-source; running it at 12V instead of 8V will probably impact it's long-term reliability somewhat, but probably did not destroy it. The resistor you want to add as noted by Mike will be roughly 910 ohms (standard value); you can go as low as 510 ohms.