When Hardison is doing the magic trick at the end of the show he says Parker's Queen of Spades is the card and pulls up a seven of clubs. The scene cuts to Parker holding the Queen and when Hardison is shown again he is holding a ten of diamonds.
Patents are public records. (Trade Secrets aren't.)
When Parker uses the cable to drop down the elevator shaft, Elliot clips the other end to Hardison's belt, which subsequently causes him to be pulled up to the ceiling of the elevator and get anchored to the ceiling against the roof door. The only way this could happen is if Parker were heavier than him. Simple physics dictates that given their comparable mass, Hardison would just get a strong jolt but would not be carried upward into the air, certainly not more than just briefly tugged.
When Markland is chasing Dr Jamison, he comes to the elevator and pushes the metal plate to call an elevator, instead of pushing an elevator call button.
When the con is 'blown' and Eliot is battling the security staff in the elevator, they contact the VP over the radio identifying Eliot as 'the magician's assistant.' They wouldn't know Eliot was part of the magician's crew since he was smuggled in with the gear, he had already been seen as the pizza delivery person earlier so couldn't walk in on his own.
In the final exposition, it shows Nate telling Hardison about the food patents when Hardison is in the locked room. But later it shows Hardison downloading the patents to Casten's phone while Casten is in the server room, which happened earlier.