The "R" sound in the word "Zorro" is pronounced as a hard, rolled "R". When Elena pronounces it, she pronounces it with a soft "R". A woman raised in Spain, as her character is, would definitely not pronounce it this way.
In the end of the movie, when Zorro, Elena and Armand are fighting on the front part of the train, they have a structure ahead of them (the one they will grab to get off the train). However, when camera shows us the view straight forward of the train, the structure is not there. In the following angles it appears to be there again.
In the fight scene on the train near the end of the movie, the engineer is thrown forward, pushing the throttle in the cab of the locomotive forward. This has the effect of making the locomotive go faster, when in fact, the train should have stopped. Pulling the throttle back would have made the train go faster. Also, opening the throttle, as was the intent, will lower steam pressure - not rapidly raise it as shown. The only way to raise steam pressure is to add fuel to the fire. Using steam (as in going faster) lowers steam pressure.
Telegraph wires connected the east and west coasts in 1861. Even if a telegraph message were relayed to the hidden receiver, it would have only been able to print a coded message, similar to Morse code, onto the ticker tape.
The Pinkerton agents claim that since California has not obtained statehood, U.S. authorities don't have jurisdiction to get a search warrant. But California in early 1850 is a USA territory where federal agents have just as much jurisdiction as in states. Furthermore, "Pinkertons" were not employed by the federal government until 1861.