The position of the baby changes between shots, with no time for that to happen.
When Sam and Al are in the bathroom before the suicide attempt, Sam turns on the water in the bathtub which you hear running under the dialogue. When he sits on the edge of the tub and reaches to turn off the water, he doesn't actually turn the tap .
On the day of President Kennedy's assassination, there is a sign on top of the Texas School Book Depository that advertises for Hertz and Ford. The sign actually was an advertisement for Hertz and Chevrolet.
A baby is heard crying, but no shots of the baby's face show tears, or even unhappiness.
In the Book Depository, Al's shadow is seen on Sam.
At index 36:55 two 80's vintage cars are seen driving. One is an Oldsmobile and the other possibly a Ford.
Project Quantum Leap's present date is given as February 15, 1999. However, this is seven months before the present date of September 18, 1999 given in The Leap Back - June 15, 1945 (1991).
There is no location for the meeting on the Save Cuba leaflets that Oswald is passing out.