When Sam is playing the guitar his hand is halfway up the fret board but Maxwell's hand in the reflection is at the top of the fret board.
In Tim's bedroom, there is a Rolling Stones "lips/tongue" poster. This popular trademarked logo did not exist in 1966. The logo was created by John Pasche in 1970 for the group and wasn't available as a poster until at least 1971 or 1972.
Sam tells Tim, in May of 1966, that he will be able to hear Jimi Hendrix within the year, at Woodstock. Hendrix's career was in its early stages in 1966 and Tim might have caught a performance in Greenwich Village, but Woodstock wasn't until August 1969.
Tim Stoddard mentions the moon was in its first quarter. On May 21, 1966 it was one day past the new moon.
Al being a hologram should not cast a shadow, however he frequently does which means he is blocking light; this would be seen by anyone in his vicinity. shadows are also cast onto Al, for example the very end of S05-E06 when Sam stands in front of Al as the spaceship arrives, shadow is cast on Al's white suit.
John Stoddard claims that his father Maxwell emigrated from Ireland to the United States to escape the Great Famine. However, Maxwell was born in 1887 while the Famine lasted from 1845 to 1852.
Although this episode takes place in 1966, the novels "The Greek" (1973) by Pierre Rey and "Serpentine" (1979) by Thomas Thompson can be seen on Maxwell Stoddard's bookcase.
When Sam says "Oh boy, oh boy!" in the teaser at the beginning of the episode, his lips don't match the audio.