In Ted, When the news shows Ted being arrested at an airport. Ted gives the camera the rude finger. When he does this, his hand is censored. Ted doesn't actually have any fingers then how would he have been able to show a finger?
Ted's paws are shown throughout the film as being very prehensile. He can:
Among other complex hand tasks.
It is conceivable that if he were to point his paw in a certain manner at a person or a camera that the gesture could be perceived as him giving the "finger" (technically the paw) to the viewer. In the scene where he does (he's being detained at an airport) it is clear that he is also complaining very loudly and cursing , so it a gesture with his paw might be seen as him flipping off the camera.