When pursuing a white van, the coffee cup in Vicki's hand disappears.
The judge releases several suspects on their own recognizance due to an issue with "prison overcrowding." Suspects awaiting trial are not sent to prison, they are held in jail. Prisons are for convicted criminals usually serving sentences of a year or more.
The crime scene investigator says that the "cuff marks" on Weeks' wrists were at least 3 days old. The sort of impression that handcuffs leave on the skin would not last 3 days. They would be gone in a matter of hours if not minutes.
The "coffee" that the officers pour down Nelson's throat is obviously just water.
While driving, the two police officers are drinking from empty cups.
Two officers, male and female, admit they have romantic feelings for one another but cannot act on it due to her being married. They say there is nothing they can do and they must ride around in a car together all day without acting on their feelings. One or both of them could contact the scheduling desk and request to be assigned a new partner. While such requests are not always honored by police departments, it would at least be worth trying.
LaRusso complains that the other officers "screwed up the bust" by entering the suspect's house without a warrant. A warrant is not needed for an officer to enter a home if they have a reasonable belief of an imminent danger. The officers had every reason to believe that Weeks was armed and would attack them, as he had already done to one officer the previous day.