When Eliot asks the waitress for a couple of beers he waves at the 2 Irishmen with nothing in his right hand but in the next shot he is holding 2 darts.
When Nate approaches the card players in the back room, he says "Gentleman, I have a proposal for you" and there is a commercial break. When the break ends, the line is repeated-- but with completely different inflection.
When Mark Doyle shows Tara his bag of cash bundles, the $100 bills have Ulysses S. Grant pictured and the $20 bills have Benjamin Franklin. In reality, Benjamin Franklin is on the $100 bill and Andrew Jackson is on the $20 bill. The bills are also of an old design, with the faces in the center of the bill; as of 2009, when this episode is set, both $20s and $100s had been updated to the current design, with larger faces offset to the left.
When Hardison pulls the green blanket off the TVs, it sticks, revealing that it had been taped up, so it didn't fall during filming. With the time crunch Hardison was under, he would not have taken the time to secure it.
The whole story is that the loan shark will take the restaurant in place of the money owed. In reality, s2.e1 Hardison explains he bought the building and is now the landlord. Legally, the bar couldn't have been seized.
When Doyle pulls his pistol on Nate at the poker table, you can hear the sound of the hammer being pulled back. Yet you never see Doyle touch the hammer, and when the camera moves to behind Doyle, the hammer is still up.