I believe whether it shows the tab is dependent upon whether the status bar is visible. i.e. if it's a full screen app like the camera, where you don't see the status bar at all, or a video, where you don't have a status bar unless you tap. Basically, if you don't see the status bar, you'll get the tab and have to swipe twice to get the notification center.
As for accidental swipes, no, I haven't had any accidental swipes. At least not since before the beta where they made it so you have to swipe twice for full screen apps. Even then, my only issue was with the camera, when switching from video to still while in landscape (where the switch is pretty close to the top of the screen).
I never run into it when scrolling because I always start my swipes in the middle of the screen anyway. I'm a pretty short swiper, maybe about an inch at the most. I rely on the momentum/acceleration if I need to scroll a lot.
(oh, how many times I thought to myself, "that's what she said")