Can an object appear to travel faster than the speed of light? An object cannot travel faster than the speed of light.
But given a video of an object travelling at $0.5c$, could one speed the video up so that the object appeared to be travelling at $1c$, $2c$ or more?
Or would something prevent this?
 A: No. There is nothing to prevent such faster than light appearances. The rule is simple: No actual thing (information) can travel at a speed greater than the speed of light. 
When the considered particle appears to travel at a speed greater than the speed of light in your video, there is a non-local distribution of information - set up a priori. This distribution exhibits itself as something travelling at a speed greater than that of light. But no actual particle/information travels at a speed greater than the speed of light in this entire scenario. 
A: Nothing can prevent you from speeding up the video, but there are ways to tell if you are looking at a sped-up video or at a real video of an object traveling at a speed close to or equal to $c$ (or greater than $c$, if we can assign any meaning to this concept). 
Think about length contraction: if you are looking at a spaceship traveling at a speed $v$, from your frame of reference its length in the direction of motion will appear to be
$$L = \frac {L_0} \gamma = L_0 \sqrt{1-v^2/c^2}$$
where $L_0$ is the length of the spaceship in its rest frame.
If $v \in [0,c]$, $\gamma >1$, so the spaceship will appear shorter to you. If $v=c$, we would have $L=0$: the spaceship will look like a segment from your frame of reference (the contraction only happens in the direction of motion, so it would appear like a segment and not like a point). 
This shortening effect will not be present in a sped-up video, so you would be able to tell if the video is really showing a spaceship moving at a speed close to $c$ or just a sped-up version of the same video.
If $v>c$, the formula above breaks down because $\gamma$ becomes imaginary, but you would still be able to tell a sped-up video from a real one...also because you know that no physical object can travel at a speed $v>c$.
