It looks like you didn't solder the last two backlight pins towards the middle of the LCD header on the back side.
Actually, I think that is the monochrome version of the display. It only has 16 pins.
The soldering on the display part looks fine. The rest (buttons and processor) are out of focus. Can you post a clearer shot of that part of the soldering?
From the symptoms you describe, I suspect that a marginal connection may have left the right button 'floating' so that it picks up spurious signals when you press other buttons.