In the opening scene, Mac chases down a man who shot someone. When he catches up with this perp, he uses a plastic bag in lieu of handcuffs, which makes sense since he's wearing a tuxedo. During the arrest, the perp's gun falls to the sidewalk. However, when Mac walks away with the criminal, he fails to pick up the gun - a mistake no police officer would commit.
The newspaper shows the deceased deputy mayor with the headline "just desserts." This is a common misspelling and should read "just deserts." In this case, the word deserts comes from the word "deserve."
When Stella and Lindsay are walking down the hall, Stella receives a phone call from Hawkes. When she answers the phone and puts it up to her ear, you can see the main menu which means she never actually answered a call and isn't really talking on the phone.