When Hardison enters the shop, Elliot has to buzz him in, indicating the door is locked. After Hardison subdues Elliot, the Russian goons just walk in as if the door wasn't locked.
When Hardison is in the vault, he is unable to open box #72 before Kerrity shows up. But when the cops enter the vault, box #72 is open.
When Parker and Hardison escape by blowing a hole in the floor there is understandable dust and debris in their hair and on their clothes but when they exit the tunnel they are perfectly clean again.
Since Hardison and the crew can communicate via their ear buds, he shouldn't have needed to call Sophie to alert them to his abduction by the Russians.
When the Russians leader and Hardison take shots, the cuts back and forth show their shot glasses are full again.
When the Russian thief drinks with a handcuffed Hardison, he says "Na zdorovie", when the correct phrase is actually "Za zdorovie". It's a pretty common mistake for non-native speakers.
After Hardison 'removes' the serial number from the diamond, Kerrity examines the bottom of the diamond. The serial number was etched on the girdle (side), right where he was holding it.
Hardison describes the laser as UV (Ultraviolet), but the safety placard identifies it as CO2, which is infrared.