Monday’s episode of “Quantum Leap” was set in 1989 aboard what the script and visual effects intend to be the USS Montana, BB-77. According to the US Navy’s battleships page, that vessel doesn’t exist, although Wikipedia says that “Montana-class battleships” reached the design stage.
Due to a few seconds of video that technically creates a continuity error, I can tell that at least some of the action was filmed on a real battleship, one that just so happens to be docked in Los Angeles.
That’s BB-61, the Battleship of Presidents, the USS Iowa.