Maintain Your Frame
Assuming that you've set up your shot well, now you have the additional problem of maintaining it. Unlike with still photography, with video you don't just frame one shot—instead, you frame 30 shots per second. Because the iPhone is so light, it's very easy to reposition. For the same reason, though, it's very easy to reposition accidentally, causing shaky footage, accidental new angles, and so on. Vigilance is warranted with regard to framing.
Once you've started the video camera rolling, make a regular effort to pull your focus—your visual focus, not your camera's focus—from your subject, sweeping your eyes around the edge of your frame to make sure that you have a clean shot and the right headroom. Scan for lines that might make your shot more compelling, and consider changing the angle of your shot (especially if you plan to edit the video later).
How often you need to recheck your framing depends on how fast you and your subject are moving, but ideally you shouldn't let a moving shot get repositioned without stopping to check. It can be surprisingly difficult to pull your eyes off your subject—almost as if the subject might disappear if you don't stare intently at it. It won't, though, I promise. Make the effort to sweep your eyes across the screen and reframe as necessary.