When Chicago's Sears Tower is visible for the first time during Danila's arrival, it is dusk. However, the ride is then extended another day and Danila is finally shown arriving in Chicago during the day.
The Jeep Grand Cherokee that's chasing Danila and Victor is not the same one that gets machine gunned in the alley. In fact it is an older Cherokee with different rims.
When Danila's plane is shown taking off from Moscow on a way to New York, it is a Boeing 737. Boeing 737 is not capable of flying Moscow to New York non-stop due to its limited range.
The supposingly "Chicago" hockey scenes were actually shot at the Civic arena in Pittsburgh (the home of Pittsburgh Penguins).