This is the wiring:
No. That is a drawing of how the wires should be connected. We need to be able to follow your actual wires on the actual hardware.
Here are the PCB traces:
Unfortunately that picture doesn't show which pins D4, D5 and D6 go to on the connector, and the connections on the other side of the board are hidden under the display. What did you come up with and have you double checked? One would assume the pins are sequential but you never can tell.
EDIT: Comparing the board to the fritzing diagram it looks like the connections in your diagram make sense and the pins are not quite sequential. Are you SURE you connected them correctly?
Under what conditions does your display show weird characters? As long as something shows up under some conditions we can assume that the contrast setting (controlled by R2 and R3) is OK.
Just curious, why did you replace the display on your printer?
Don