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The inconsistent timeline: many stories show characters going back in time, changing something, and then going back to a different future. If the characters are in the same probability chain, this is impossible because anything that had been done in the past will already be incorporated into the future that they once came from. Therefore, they could not have returned to a different future, since the future from where they came and the future they returned to must be the same if they do not become unstuck in probability.
The spatial inconsistency: a person travels back in time to their exact location in space. This is physically impossible if the time machine only moves in time. Our planet and our galaxy is constantly moving, so we cannot ever return to the exact spatial coordinates we were once at at any given point in time. Therefore, if a character has a time machine that only moves in time, they will come out in empty space when they time travel through years.
The bootstrap inconsistency: when a character goes back in time and gives himself or herself an object. The object then has no discernible origin because of the following reasons: it could not have originated from the past because it was given to the character by someone from the future and it could not have originated from the future because the past self had it in his or her possession in order to go back and time to give it to themselves in the first place.