While Logan is editing the tribute video to Lilly, among the video clips is one that shows her as a little girl between the age of 5 and 7 at Legoland California. Legoland California wasn't in operation until 1999, which means that Lilly would had to have at been least 10 or 11 during the visit, making her too old to have appeared in the aforementioned clip.
When Veronica wakes up after having crashed her car in "Leave it to Beaver", she is shown to be wearing her seat belt. When she immediately reaches to grab the tapes and her cell phone, however, her seat belt is no longer on.
In "Credit Where Credit is Due" when Sheriff Lamb leaves the diner, Veronica says, "Smell you later." Veronica puts her cap on as the Sheriff walks out but then we see her without her cap on. As her dad responds, "Smell you later?" she puts her cap on again.
After Celeste turns to leave Mars Investigations in pilot episode, the camera focuses on Keith Mars. On the left side of the screen, you can see Celeste turn to leave, yet she is already walking towards the door right before this.
In episode "My Mother, The Fiend", Veronica and Mary are typing to each other on Veronica's laptop. Veronica writes "What did my mother do to hurt you?" to which Mary replies "Hurt? Your mother was my friend". Mary doesn't press the H key on the keyboard to start the sentence which is obviously needed to write the first word.