When Claire is jogging in the park, the man who runs up next to her has only a small amount of sweat on his chest. After only a short period of jogging, the amount of sweat almost covers his whole shirt front. This is most likely due to many takes being done.
Though this was arguably one of the most powerful entries in the series, the entire premise is fictitious. No one has been executed by the state of New York since 1963.
When McCoy gets out of Claire's car, he flips his seat belt from his right shoulder over his head and onto his left and then gets out of the passenger side. He should not have been able to do this with the mandatory lap belt in the 3 point restraint.
At approx. 16 mins, Jack and Dr Olivet are in the restaurant. Jack orders a "scotch, rocks", and when he orders food, the drink appears at the same time (at warp speed).
Attica Penitentiary is not located in Suburban New York City, but in Western New York State and is at least a six hour drive from Manhattan. so the premise of the episode if execution occurred at 12:22A.M. the crew would have had an all night drive back to the city and would have been extremely tired , thus accounting for the emotional and sudden mood swings experienced by the crew. Had the execution occurred at 12:22 P.M. the crew would have either taken a private jet to and from rural Attica or driven at warp speed to return to the city by mid afternoon.
When DA Schiff holds the press conference, he says the prisoner died at 12:22AM. The execution occurred during the day. So the time had to have been 12:22PM.