Throughout the series you can often hear the actress (Majel Barrett) who performs the voice of the computer taking breaths between lines. Obviously a human actress would have to do this, but a computer with an electronically generated voice would not, as it wouldn't breathe.
It is claimed that Data can't use contractions (Can't, Isn't, Don't, etc) yet there are several instances throughout the series where he does. One of the first such examples is heard in Star Trek: The Next Generation: Encounter at Farpoint, where Data uses the word "Can't" while the Enterprise is being chased by Q's "ship".
Very often star streaks are seen backward. Ignoring tunneling (something that would have been hard to do in the late 80's) when moving faster than light speed stars would look streaked as depicted, but they would be blue as you approach the star and red after you pass. Sometimes this is depicted correctly but others it is seen the other way around.