The twitching is known as GLITCHING. Funny how that rhymed.
At any rate, bad batteries, loose connections, outside radio interference, faulty failsafes, loose metal to metal contact, bare wire to metal chassis or other metal part contact, and a number of other small detail oriented issues can cause it.
I'd start by removing the failsafe from the problem (just take it off vice bypassing it...unless that is what you did to bypass it).
Next, I'd replace the batteries or ensure a fully charged set were in use.
Next, I'd check all wiring for chaffing or loose connectivity. Any bare wiring, I'd tape up or shrink wrap as appropriate. Loose connectors just need to be snugged up.
From there, I'd check all metal to metal contact and ensure that the screws or fasteners that are holding that metal to metal contact are tightened down all the way so there is no way for the metal to vibrate against the other metal.
If the problem still exists, check for an outside interference source (high power lines, cell phone towers, radio towers, cordless phone in the house, etc). If this happens uniformly where-ever you go (in the house, outside, anywhere), then you need to re-check the above again...and perhaps think of getting a new servo. Why? Sometimes servos start to glitch as they are about to go bad.