The book Allison gets as a gift is titled "From the Earth to Moon"; the actual book by Verne is titled "From the Earth to the Moon".
The Frankel Footage was on Kodak Kodachrome film stock which was only processed by Kodak's laboratories and could not have been processed by Morty himself in his darkroom and so could not subsequently viewed by him. It was normal to be sent away for processing, which would take several days.
When Klaus stole the pickup truck keys and was running through the parking lot he ran past a 1966 Ford Truck even though he was in 1961.
When Hazel is telling Five about doomsday several extras appear and disappear between shots. One woman is seen approaching Five from behind three different times.
Modern LED streetlamps can be clearly seen in various street scenes.
When the Hargreeves land in Dallas in the 1960s, it is stated that they land in the alleyway at Commerce and Knox. Not only do Commerce and Knox not intersect in Dallas, they are in fact 5 miles from each other running almost parallel to one another.