Responding to rwillia532a, could be a parallax error but disagree with the statement that it "physically must happen". My Canon 24-200 SLR lens has barrel distortion at the widest range, arguably something that "must" happen on a lens with such a huge zoom range. However, Canon digitally corrects it so that, as long as the photos are viewed through their software, the problem is unnoticable. Horrible design on Apple's part. Inexcusable really.
Responding to Dogcow-Moof, that 100% wrong that it can't be fixed. It CAN be addressed with software correction but Apple has been too lazy to do that. See comments above about digitally correcting barrel distortion. If barrel distortion can be digitally corrected, so can parallax error. Explaining why video looks like crap when the zoom crosses from one lens to another doesn't excuse the problem.
I'm not sure it's even parallax error at all. As you said, when you switch from one eye to another, an object appears to move. The problem I'm seeing isn't so much a motion problem as a change in brightness and clarity. I think the actual problem is a difference in quality between the primary lens and the "secondary" telephoto and macro lenses. I've noticed in low light shooting, inside museums for example, that the secondary lenses are not as bright as the primary lens. I don't think they capable of opening to as wide an aperture (because they're inferior lenses due to Apple cutting corners) so you see a difference in brightness at the lens switch.
Responding to mega-watts, bingo! It's an Explanation not an Excuse. The bank can Explain how your deposit inadvertently went into someone else's account, but that situation is still Inexcusable and the bank needs to resolve it. Explaining why video looks like crap when the zoom changes from one lens to another does not excuse the problem.
Regarding the numerous comments referencing Apple's reply that it is just to be expected, absolutely pathetic. Other multi-camera phones don't have this problem. Just another example of how Apple doesn't live up to the hype and isn't worth the money.