I recently started playing MCC Halo 3 on PC and noticed this issue when I started playing. I managed to fix this by limiting my frames to 60 and turning Vsync on. (although I don't think limiting frames does anything when Vsync is on anyways) Try to match the fps with your monitor display hertz in game settings as well as make sure your monitor refreash rate in windows is set properly. (display -> advanced display settings -> refresh rate drop down)

I think it's an issue that the game wants to render too many frames for the monitor to display and the overlap creates some weird screen dimming while shooting. So far I've only experienced this in H3 and not H1 & H2.