Continuity mistake: The second time the day happens, the man stands up in the restaurant to profess his love to his girlfriend almost immediately after the waiter drops his tray. There is only about ten seconds between the two events, but the first time it all happened, there was a gap of nearly thirty seconds.
Continuity mistake: When Tru and Harrison talk on the phone near the beginning of the day's second incarnation, it is pouring rain where Harrison is, and he's standing under an awning. It's not raining by Tru - or at least not enough to be noticed by the camera or to get her wet, which isn't a problem in and of itself, except that everybody around Tru is carrying umbrellas for some reason.
Continuity mistake: The first time Tru lives the day, she has breakfast with her brother first thing in the morning. Harrison goes to put sugar in his coffee and the lid falls off. The second time, they go out together much later (after Tru goes shopping with Lindsay), and Tru manages to grab the sugar lid just before it falls off. But people have been eating at the restaurant all day, so it's not at all likely that the lid would still have been loose. Plus, the same patrons are seen in the diner even though it should be a completely different crowd.
Star Crossed - S1-E6
Continuity mistake: Tru tells Davis that she's "never had anyone help [her] before." But Harrison has helped her in almost the exact same way as Davis does, in most of the episodes so far.
Continuity mistake: Harrison and Melissa are in a poker game. In the scene where her flush beats his pair of fives, they each have the eight of spades in their hand.
Continuity mistake: Near the end of the episode, Paige asks Tru something along the lines of "aren't you going to tell me your real name?", showing Tru hasn't told Paige her name yet. But then Paige says "goodbye Tru" at the end of the scene.
Continuity mistake: The first time Tru goes to the reunion, she wears a colorfully decorated beige blouse with a knee-length black skirt. But when she jumps into the pool upon seeing Candace's body in it, she's suddenly wearing a white top and full-length pants, which happens to be the outfit she wears the second time she goes to the reunion.
Continuity mistake: When Tru, Jack and Davis visit the car salesman she says that she worked at the 'county', but on their jackets it says 'City Morgue'.
Continuity mistake: The clock in the MCAT testing room reads 10:55 when the test starts without Tru, and 5:05 when the proctor tells Tru that she's more than three hours late. But by those clocks, she's actually more than six hours late.
Continuity mistake: When Marco brings in Jake's body, he says that Jake was given a "clean bill of health" after the removal of a bullet from his leg. However, we later find out that a bullet fragment was subsequently found in his leg and that an embolism had formed.
Chosen answer: The next episode shows that Tru didn't meet Luc after all, even though she should have been in work by the time he showed up. I think the answer is that the writers don't actually know.
DavidK93