In general, it’s a bad idea to re-solder connections unless you have a specific reason to do so. We’ve seen quite a few boards destroyed by unnecessary re-soldering.
You can use your multimeter (with the Bulbdial unplugged) to check the resistance between the different lines. Look at the circuit diagram, and make sure that (for example) the resistance from pin 16 of the chip to control line LED10 is 68 ohms, and that the resistance from pin 15 to LED 8 is 24 ohms. Also make sure that there is high resistance between any two of the signal lines that go to the red board.
