Nice to see that you have a sense of humor (Hmmm...are you stalling over Monday's assignment? ;-)
Why no stage separation and why is it still visible to a $900 Nikon several minutes after launch?
I'm not a ballistics expert (and don't play one on TV) but is it possible that the video of the "missile" launch was taken during a prolonged stage one? It's my understanding that while a missile is trying to gain altitude, it is much slower than at it's top speed.
There is also a possibility that the stage two booster rocket you're looking for failed as well and the thing fizzled. And just maybe the entire launching was half-assed by design.
It still does NOT appear to be a jet.
As to your question regarding why a Nikon could still catch a glimpse several minutes later, I'm sorry I haven't an answer for you.
The answer is that the object was coming toward CA -- not out to sea. That's because it was an incoming MD-11 flight from Hawaii to Ontario, California...
No, you can't film the passage of a rocket after it's gone out of sight! On the other hand, you can film the flight of an airplane for many minutes.