Assuming you were only cited for the speeding:
- A continuance (postpone) is not automatic. When it's time for your trial, the DA will have to request for it, saying something like "my witness is not here, I'd like to request to continue...". You should have objected, citing how it inconveniences you, arguing that this is just a small traffic case and so on. Basically, object VIGOROUSLY at this point.
- If the judge agrees, great. If the trial continues, you'll most likely be dismissed since there's no witness testimony.
- If the judge disagrees and force a continuance on you, well then just go ahead with it. Chances are the office won't show up again. This time be prepared to object even more vigorously to a reschedule. 99% change the judge will listen this time.
To answer your questions, no the DA didn't lie, and there's nothing for you to check. Maybe he's screwed up his witness's schedule, maybe not, but that's beyond the point. The point is that to your great benefits, the prosecution showed up without a witness, and you should have taken advantage of that, thwarted any rescheduling attempt, and possibly won your a dismissal.
Well it's too late now, but remember it next time. Otherwise just proceed with your original defense (you did come to the original trial with a good defense, right? Don't say your only defense was to "expose" the screw-ups by the DA)
If you didn't waive your speedy right then another ground for dismissal is if the retrial falls outside of 45d from arraignment. There are already lots of info about this elsewhere.

