Flanagan (Garcia) says the late edition that had the murder of James Withmour was dated April 18th, but the newspaper slide has the date Tuesday April 19th. That date is also inconsistent with the previous newspaper slide, which had the date Thursday April 10th.
When Steve Sr. is looking at the photo of Lila for the first time, the cigarette goes between in and out of his mouth between shots.
The edition of the newspaper announcing Whitmour's new Rolls-Royce Phantom II is dated Thursday, April 10, 1932. That date was on a Sunday.
O'Loughlin and Caan retain their modern stubble in the flashbacks. In 1941, men--especially police officers--never looked this way (unless they were bums); either they were clean-shaven or had full beards.
During the nightclub sequence, Meaghan Rath's arm tattoos are clearly visible. Women simply did not get tattooed in those days.
Alexa Alani's (Rath) cigarette has a filter. The outside is white but is clearly a modern, white filter and not tobacco at the end as she rises it. The cigarette is also too long to be a non-filtered. (Although filters where introduced in 1935, they where exclusive, and made of cork. Modern, white filters did not come in use until 1954.)
A modern range cooktop is clearly visible as Steve goes through the mansion at the end.
When the trio goes to the "Whitmour compound" in a pickup truck, a modern streetlight is visible, upper right of the frame. And, a modern street sign is visible in the background as they exit the truck.