(This is a wiki post, please add and correct!)
Inspect your work. Verify all components are correct values. Look for solder connections that are rough, irregular, skimpy, dull, or missed completely (we all do that!) and reflow them. Look for solder bridges between pads and remove them.
Check your cable. Make sure the red stripe connects to the -12V pins at both ends (module and power supply or bus board).
Disconnect power and check for shorts:
Something not addressed in that video is: If there are 10R resistors or diodes in series on the power rails, shorts elsewhere in the module will not be found by checking at the power header. Check again at the other sides of the resistors or diodes.
Also make sure there are no shorts in the cable between ±12V/ground.
Make sure all ICs are oriented correctly, not in the socket backwards. Make sure they are seated properly and all pins are actually in the socket, not bent under.
Make sure all diodes, transistors, voltage regulators, voltage references, and polarized capacitors are oriented correctly. Double check if you’ve substituted one transistor type for another: the two types may have different pinouts.
Check continuity between the power header and the ICs: Make sure the +12V pin connects to +12V, the -12V pin connects to -12V, ground pin to ground, +5V pin if any to 5V regulator. Check the datasheet or ask here if you don’t know which IC pin is supposed to connect to each. Again, if there are series resistors or diodes on the power rails, you will need to check continuity from the other sides of those.
Connect power and check to make sure no components get hot, or start to smoke or smell. If so, disconnect power and don’t connect again until you’re confident you’ve found and fixed the problem.
With power on, check the IC power pins again, this time to see if the proper voltage is there. Measure with the red probe on the IC pin and the black probe on a point that connects to the power supply ground.