Yep, its called Cherenkov radiation, light emitted by particles moving faster than light in their current medium. In real life this is impossible in a vacuum, but in some materials (such as water) high energy radiation can travel faster than the local speed of light. It looks a bit like this:
That's an active reactor core in a deep water tank.
Are there any other theoretical tell tale signs that something had travelled faster than light as opposed to just "Really really fast"?
Well, its hard to be really certain about this, because superluminal travel is problematic for many, many reasons discussed elsewhere, but here are a few thoughts.
With a ship flying towards to, as it has travelled faster than its own light, you'll be able to see the light it had emitted catching up with it. The light emitted most recently will arrive first, then light emitted earlier. This means that you'll see an "echo" of the ship shooting backwards away from you into the far distance. There's a non-FTL effect a little like this called a light echo. The "echo" will propagate pretty quickly, so I'm not sure whether you'd be able to see the effect unless the ship was travelling over a very long distance (eg. lightseconds or more).
A ship flying away from you won't show this effect, as the further away it gets the longer the light will take to reach you.
Things will probably get even weirder if you observe a flyby rather than an arrival. The first light you'll see will be from where the ship was at its closest point towards you. Then _ think you'll see the FTL-light echo receding from you, and the light of its flight away from you at the same time. If you couldn't tell front from back, it might look as if two ships appeared together and shot off in opposite directions.
Now, there are of course issues of blue- and red-shifting, but it isn't at all obvious to me that you'd see those effects on a superluminal object (inasmuch as it is possible to even have a superluminal object you could see) but as things have already tottered out over the cliff of plausibility, you could probably handwave that as you wished.