When Sam looks into the mirror for the first time and sees himself as Frankie, he is wearing pants and a shirt. He reaches over to grab his suit jacket and when he faces the mirror again, he's wearing a cummerbund that wasn't there a second ago.
Al says that it is hot in the imaging chamber because Ziggy shut down all non-vital electrical systems, including air conditioning. However, computers require air conditioning so they don't overheat and automatically shut down.
In Double Identity they say that Frankie is the first born son of his family, yet his brothers are named Primo and Segundo which means "first" and "second" in Italian. They would probably only have been named this if they were the first and second children of the family, not the second and third.
At 5.15pm, Sam indicates to Theresa that he can see Betelgeuse out of the window. However, in early November and at this latitude, Betelgeuse does not rise until approximately 8pm.
The episode "Double Identity" (1.5) takes place in early November of 1965, yet a theater marquee says Doctor Zhivago (1965) is playing. It wasn't released in the United States until the 22nd of December.
Sam Beckett (Scott Bakula) is wearing some sort of earpiece device in his right ear while singing "Volare" early in the episode's wedding scene.
Sam claims that he was ten years old on November 8, 1965. However, in Genesis: Part 2 - September 13, 1956 (1989), his date of birth is given as August 8, 1953.