Continuity mistake: While camping and searching for horcruxes, the size of the trio's tent changes from location to location. Harry is standing beside it while Ron and Hermione are skipping stones across a body of water, and the tent is fairly tall. Other times, it's very short like a pup tent and they must stoop to enter.
Continuity mistake: When Harry jumps on the dragon, his hair is wet and messed, then it changes to dry and brushed and in the next angle, for a brief moment, it's back to wet and messed.
Chosen answer: Hermione knows this is an unusual request and she and (and Harry) suspect the bank knows that Bellatrix's wand was captured by Harry Potter (at the end of Part 1). Showing the bank manager the real wand would prove that this is not Bellatrix. The bank and Voldemort's minions expected that Harry and the others might go to Gringotts searching for a Horcrux in the Lestrange's vault. They are setting a trap for Harry and his accomplices.
raywest ★
Incidentally, if I remember right, in the book Hermione actually does hand over Bellatrix's wand, not realizing the Gringotts goblins already know the wand is no longer in her possession, forcing Harry to cast a timely Imperius Curse to avoid the entire plan being exposed.