We have a 100 nF decoupling cap across the PIC power supply pins, but no electrolytic specifically dedicated to the PIC. A 47µF cap seems to me to be a bit excessive for decoupling a single device.
The glitches are a series of 2 µs wide positive going spikes, spaced about 300 µs apart. Looks like there are about 20 of them, from what I can tell from the grainy digital scope trace they sent me. I hate digital scopes. The glitch pulses are all equal amplitude with the peak at about 66% of Vcc. They are all exactly the same amplitude; they don't don't decrease. So, I'm ruling out ringing. This spurious signal lasts for about 6 ms before the output actually transitions from 0 to 1. At the moment, I'm not entirely sure if these spikes begin at the time when the output is supposed to transition or if they end at that point. Sorry if I sound vague, I'm still trying to understand the information I've been sent.