While on the rifle range, the Sergeant hands Lee Harvey Oswald (Dr. Sam Beckett) a clip of blank ammunition (red wadding). When Oswald then loads his rifle, the clip of ammunition resembles live ammunition.
When Sam (as Lee Harvey Oswald) is talking to Ellie on the street in New Orleans she noticed Oswald is married due to a wedding ring in his left hand. Having gotten married in Russia to a Russian the wedding ring would've been on the right hand as is tradition in Russia.
Marina tells Oswald (Sam) about how many words, in Russian, he knows. But, in fact, Oswald was so fluent in Russian, when Oswald met Marina, she actually believed he was a Native Russian. Not a goof: Marina is counting how many *English* that words *she* knows.
This episode puts the date at project Quantum Leap at February 14 1999. If this was true then time would be going backwards for the people working at the project since in Season 4 Episode 1 "The Leap Back" the date was September 18 1999.
At the beginning of the episode, Sam (as Lee Harvey Oswald) is on the firing range in Japan on Oct 5, 1957. The US flag flying from the spotter tower is a 49-star flag. That flag was created for the inclusion of Alaska as a state, but Alaska wasn't granted statehood until Jan 3, 1959.
When Sam discusses with Al the possibility of being in the Texas School Book Depository in Oswald's place and says, "I could stop the assassination," his lips don't move.
"GRANDFATHER PARADOX" of Time Travel: If Sam had NOT prevented Lee Harvey Oswald from shooting and killing Sergeant Lopez in a bar in Japan in front of other Marines in 1957, Oswald would likely have been executed or sentenced to life imprisonment, or at the very least sentenced to several decades in prison. He certainly would not have had the opportunity to assassinate JFK on November 22, 1963. Neither would he have defected to the Soviet Union and met and married his wife Marina, and therefore she would not have taken the notorious pictures of him with his guns, as depicted at the start of this episode. Therefore Sam and Al would have never heard of Lee Harvey Oswald, let alone had a presidential assassination to attempt to prevent.
Project Quantum Leap's present date is given as February 14, 1999. However, this is seven months before the present date of September 18, 1999 given in The Leap Back - June 15, 1945 (1991).