ushildvl,
If you don't see the object, there is almost no way to tell at a glance what's making a particular smoke trail.
The LAX departure, if I recall correctly, goes over water. Some commercially available signaling flares can exceed 1500 ft in altitude, travel quickly and may look like a missile, and leave a smoke trail that has just that kind of "wiggle" that looks like a guided missile, especially if the winds shift at all near the ground.
So yea, any pilot including a military pilot, seeing something bright with a smoke trail flashing past, will probably have no idea exactly what it was.
If they were over water, my initial guess would be that some drunk tard in a boat (Where was SOB that weekend?) fired his flaregun at the airliner trying to be cute. Or it could even have been a boater in distress firing the gun, although that's fairly farfetched unless once again the guy was drunk because only a moron would fire a flare at an aircraft on takeoff.
If it was a missile, yikes. But chances are if something did actually happen, it was just a flare or something like that. Remember, uber-tards have been shining high powered lasers at landing airlines for years now, so some moron launching a marine flare at a plane on takeoff is certainly not an unusually unexpected event.
On a good note, there are at least 2 commercial variants of military missile defense systems being fast-tracked through R&D and certification, so hopefully high-risk airlines will have an affordable response to any potential missile threat in the next couple of years.