When Alan Shore, dancing with Denny Crane, says "Anything Denny Crane can do, I can do backwards and wearing high heels", he is quoting a comic strip (Frank and Ernest, created by Bob Thaves) about Fred Astaire and Ginger Rogers. The original line - in the 1982 cartoon - was "Sure he was great, but don't forget that Ginger Rogers did everything he did, ...backwards and in high heels."
When Denny Crane (William Shatner) opens his cell phone to respond to a call from the new woman in his life, the cell phone makes the communicator-opening sound from the original series of Star Trek (1966).