Beckett and the ship's captain say that in the hour it would take the U.S. Coast Guard to respond to stop the ship, the ship would be in international waters and outside U.S. jurisdiction. However, the U.S. Coast Guard has the authority to stop, board, and detain American ships (or ships of any registry if a US citizen on board has asked for assistance) anywhere in the world, including in international waters. A ship's captain would know this.
The Titanic-themed American cruise ship is called the R.M.S. Bentley. The "R.M.S." prefix stands for "Royal Mail Ship," and is only carried by British-owned ships that are contracted by the UK government to carry Royal Mail deliveries.
When Haley is hacking Vikram's servers, he says it will take "some time" to stop the intrusion after they trace the attack to Castle's office. simply cutting the Internet connection would suffice.
The ship's captain is wearing the stripes and cap of a U.S. Navy Admiral, not a Captain.
When Beckett finds the camera, she handles it without any gloves, possibly destroying vital forensic information.