(at around 26 mins) Micro provides Frank Castle with several guns he claims to have purchased at a gun show without a background check. This is an incredibly misleading statement, as the only firearms sales that occur without background checks are either private sales between private citizens or illegal sales between criminals. Federally licensed firearm dealers participating in gun shows are still required by law to initiate a background check on anyone attempting to purchase a firearm at a gun show. Private sales of firearms may be conducted at gun shows, but these sales are still private sales between private citizens. That they take place in the setting of a gun show is both coincidental and irrelevant. While Frank is probably indifferent about Micro's methods, but he would probably prefer not to know the details if only to maintain the ability to plausibly deny knowing how Micro acquired them in the first place.
(at around 24 mins) The slide show Det. Martin Soap shows to Agent Budiansky includes a picture of Frank Castle wearing a United States Marine Corps Dress Blue uniform with the rank of Gunnery Sergeant, but in the next slide his rank is listed as Captain.
(at around 16 mins) When the Punisher is walking down a flight of stairs to the subway, the sign behind him reads '13th Street and 5th Avenue.' There is no subway station on 13th Street and 5th Avenue in New York City.
(at around 18 mins) Castle visits a funeral of a killed FBI agent and is standing some 15 meters of the crowd opposite to agent Budiansky who could have easily seen him, as many other people who know how he looks like.