"On the arm" refers to the acceptance of a gratuity, which is generally frowned upon by the police department.
Following the death of guest star Jimmy Buffett on September 1, 2023, the repeat of this episode that aired on September 15, 2023, added a slide before the end credits that read, "In memory of Jimmy Buffett, 1946-2023. It was our honor to play with you"
The full expression Captain Terrell was referring to is "that and fifty cents will buy you a cup of coffee". It is used to indicate that something which has just been mentioned is of no value or use whatsoever.