Early in the show, Barry pushes Mort to the ground. This happens at night in a dark junkyard. The next day there is a photo of the push and it appears to have been taken during the day under the best light condition.
The counterfeit plate shows the words "TEN DOLLARS" (and everything else) in normal orientation; they should be backwards on the plate. Thus, this plate is totally useless in terms of printing any money; the money itself would come out "backwards."
Paul Drake looks at the counterfeit bill and notes that it is a 1940 series, but the closeup of the ten-dollar bill shows that it is a 1963 series with C. Douglas Dillon's name and signature. Dillon was the Secretary of the Treasury from 1961 to 1965.
The cast plate shown (used to make the counterfeit tens) would never work. Money plates are highly detailed etched thin metal so all the intricate patterns will transfer. The cast plate as shown wouldn't even be suitable for play money...
When Barry pulls in to the junkyard, the hood of the '59 Ford is damaged but in its correct position (hinged at front). After Mort lowers the car and he, Barry & Grove are talking, the hood has mysteriously pivoted 90 degrees so that the front is next to the right fender without anyone touching or unbolting it.
There is no year on the $5,000 check.
One of the persons involved in this case is being blackmailed for having circulated counterfeit money in the 1940's. The statute of limitations for counterfeiting is 5 years, and the blackmail victim gives the impression of being intelligent enough to find this out, so it is not clear why the blackmail is still being carried on in 1964, the year of this episode.