Lazar - Thanks for the quick reply.
Filesystem - I did a factory reset and I do not see the issue any more. I'll watch it for a bit to see if it pops up again.
GPIOs - I see the same behavior as the post you referenced, only I'm using GPIO 14 and 23. If they're connected to the Expansion Dock when I plug in the USB (to power it all), the amber light on the Omega will remain dark and not light up. If I disconnect them, the Omega still does not appear to boot. If I unplug the USB and the wires, I can plug the USB back in and boot the Omega without issue.
The side circuit is for a Hall Effect sensor. I'm using the +5v / GND pins from the Expansion dock to power this side circuit.
I also have the Omega hooked up to a Sunfounder 4-relay module, connected to GPIOs 6 and 7, and to the +5v / GND pins. This circuit does not prevent the Omega from booting.