In the imgur pic, the pot on the left has "1" and "2" jumpered and the pot on the right has "2" and "3" jumpered. One is increasing when turned CW and the other is decreasing with CW. Jumper them consistently.
Take them out and "pre-adjust" them to the middle.
Maybe there's some cold solder or poor flow. The "auto selector" diode (D1) is on the board's underside. I zapped one once. It failed into an "ohmmic" state and didn't rectify from then on (i.e. bi-directionally resistive -- NFG).
The Arduino mega 5V output is reading 3.94 Volts on the meter when i power it by the dc power port and if powered by USB it is 4.75 Volts. Tried another board (uno) and it had 5V on the 5V rail and shows the correct values on the sensor, looks like you found the issue. Is there anyway to make the mega actually output 5V instead of the 3.94 and 4.75 volt values on the mega board?
Looks like you have trouble with the "mega board" 5V regulator.