F3 significantly reduces the occurrence of the black polygon "seams" between the angles of the scenery as you move by, likely by enabling a higher precision rendering mode. In the early days of 3D graphics, especially with PSone and Saturn titles, the low precision calculations used to render the graphics led to all sorts of ugly artifacts and glitches. I find that toggling this mode "ON" does a good job of eliminating the distraction these glitches can cause.

With that being said, at least on my setup, having the feature "ON" can sometimes manifest other glitches around the sprite objects (the muzzle flash from the pistols is the most noteworthy), but I find these to be minor compared to the alternative.

No idea about F4... it might just be a feature to help grab screenshots.