What factors affect sniper rifle accuracy (horizontal, not bullet drop)

I think I found the answer. On PS3, high-powered scopes are steadied by pressing the L3 button (the left joystick). When I pressed the joystick, I also slightly pushed it to the right. This rightward pressure caused the vertical cross-hair to lean toward the right. Since I was shooting at a distant target, I also aimed high to compensate for bullet drop. Since the scope was tilted, adjustments along the (no longer) vertical cross-hair introduced horizontal inaccuracy.

I just have to be careful and press straight down.

By testing, I was able to get the scope reticle to lean right or left by applying left or right pressure. It is very slight, but enough to cause a miss on longer range targets.

Your controller isn't working properly. If you tap the left stick to the right while aiming you'll see your horizontal line isn't pixelated. If you let go while slightly holding right it messes up your aim. My suggestion would be buy a new controller because the joystick in the old controllers were poorly made.