It seems to be a common problem to not provide sufficient bypassing on PIC's
because they "use negligable current". There are two effects that happen when
you under-bypass a part like the PIC because they are CMOS (this is not new
btw., anyone remember the COSMAC 1802).

1) CMOS switches have low impedance, so when switching low impedance (or worse
yet capacitive) loads, if your PIC has insufficient bypass the power supply,
traces, etc. take a while (several nanoseconds) to catch up. The dip in voltage
can cause reset.

2) You should expect some very short pulses of high current when switching
capacitive or low impedance loads. This is because the output gates may turn
on/off asymetricly under adverse load conditions, causing a momentary current
path from VDD to VSS.

Proper bypasing with capacitors of various characteristics (and don't forget
proper termination of the reset line) is often a cure for this bizarre behavior.

As Scotty was so fond of saying:
"Ya canna change tha lawhz af phyzzicss, Caaptain"

- Don Lekei

PS. Of course I could be wrong, and this whole thing is a "not initializing all
registers" thing.