There are several inconsistencies between shots in the condition and position of Doyle's car after the crash, including the passenger side mirror, which is broken off in the wreck and then reappears and disappears after the car hits the yellow crash barrels.
When Gavin Lights the paper on fire and raises it to the sprinkler head, that type of sprinkler head would only discharge the water. No other heads would spray water. The reason for this is to minimize damage.
In the courtroom, the nameplate for the judge says "Judge" Arbarbanel. However, in New York State, the person who presides over an estate matter or probate proceedings is formally known as "Surrogate" not "Judge". The nameplate would reflect this and refer to the Surrogate as "Hon. Surrogate Arbaranel". The court would also be referred to by all present as "the Surrogate's court", not the "probate court".
During the late afternoon or early evening in the office, we hear a radio news summary that describes the "stock market" performance that day and mentions "Wall Street", "NASDAQ" and "the Dow". However, the movie is set on Good Friday when stock exchanges in the US (and many other countries) are closed.