I assembled the board. I have two issues
a) The 4th quadrant of master board does not respond to movements.
b) The LEDs on the second board are lit poorly

For 4th quadrant I checked and rechecked the components. They are in right place. I even changed the LM324 Chip; same workings.

I changed the phototransistor and the infrared LED same effect.

Is there a way to check for bugs, using multimeter.

Second issue is that the LEDs on the second board are lit only 50% during response.

Please let me know the solution how to check for errors.

These sound like independent problems, they should be addressed separately.

>a) The 4th quadrant of master board does not respond to movements.

Please describe what the board is doing, *exactly*-- what is it doing when it is not responding?

>I even changed the LM324 Chip; same workings.
>I changed the phototransistor and the infrared LED same effect.

It is *very* unlikely that any of these components would fail. If we include extras, it's so that you have one if you lose it or physically break it. Arbitrarily replacing components is a very effective way to end up with a permanently nonworking circuit.

Please remember the big troubleshooting hint from the manual:
"90% of assembly issues are caused by one of the following three things:

1. Component missing or in the wrong location.
2. Backwards component, e.g., phototransistor or LED.
3. Bad or missing solder joint."

(Plus, once you started desoldering, you actually need to worry about a fourth thing, which is damage to the circuit board.)

A bad solder joint remains the most likely possibility. You can definitely use your multimeter to check for continuity, to check each of your connections whether your connections from the opto components and the chip is good, and so forth. Also check the board for stray metal bits, overbent leads, or other conditions that could cause a short circuit.

>b) The LEDs on the second board are lit poorly

Can you please describe the behavior more clearly? Is it working 100% normally except for the intensity? Or, are only half of the LEDs lighting? Or all are lighting, but only half the time? Or some other behavior?