Per the title, the Staten Island Ferry is a passenger ferry service operated by the New York City Department of Transportation that runs between Manhattan Island and Staten Island. The ferry departs Manhattan from South Ferry, near Whitehall Circle, at the southernmost tip of Manhattan near Battery Park. On Staten Island, the ferry arrives and departs from St. George Ferry Terminal. The five mile journey takes about 22 minutes each way and is free of charge, but for many decades the fare was only a nickel making it the best bargain in New York City.
The cheap fare for the Staten Island Ferry - 5 cents per trip - is illustrated when the Ferryboat Officer (Stanley Farrar) reminds Fred that he gave the Officer a dollar, and they've just completed five round trips, and, as he puts it, "the dollar is up". 5 cents per trip is 10 cents per round trip; five round trips costs 50 cents, and for two people - one dollar.
When Lucy and Fred fall asleep on the Staten Island Ferry, the boat is shown in the harbor traveling to and from New York in what is probably "stock footage", not a scene filmed just for this show. First, the boat is seen going left to right, the stern in the back (of course) and the "wake" (small waves at the side of the boat) showing forward motion. When the boat is shown going in the other direction, they simply reversed the previous scene, so that now the vessel is going right to left, stern-first, with the "wake" going the wrong way.
In this episode Ethel claims to be working on her Italian, but when they are in Italy, she never uses her Italian