Throughout the filming of the series in Chicago, if you pay attention, you can see modern cars, billboards, etc. in the background of this series which takes place in the 1960s.
In the episode where Ray & Paulie receive their passports it state that Ray was born in 1947 that mean he would have been only 16 when he first runs into Torello and he is already married with children.
During the series run, you can clearly see many post 1963 cars in the background.
The Plaza Hotel wasn't constructed until 1971, but appears repeatedly in Vegas-based episodes.
All the 1959 Fords the team drive have 1964 Ford poverty hubcaps.
During the Season 1 episodes (near the end of the season) where Manny Weissborn and the other mob bosses are meeting at a country club and arguing over whether or not to get involved in the drug trade or the takeover of Las Vegas, pay close attention to the large plate glass windows. During the night-time scenes, especially when Weissborn goes into a rant, you can see the reflections of stage hands holding boom mics, running cameras, and holding up cue cards for the elderly Joseph Wiseman to read.