When Noel asks Frasier to sign his petition asking the producers of Star Trek to create a new character, Frasier agrees and says, "Television will never improve unless the viewers speak out!" Star Trek (the TV show) had been canceled in 1969 after its third season. At the time of this episode (1995), Star Trek motion pictures were being produced, but to suggest that the TV show could be altered with a new character is an error.
Noel makes the "live long and prosper" gesture with his left hand. A dedicated Trekkie such as him would know that it's supposed to be made with the right hand, IF the person is right-handed. If the person is LEFT-handed, using the left hand to make the sign is perfectly acceptable.