The background footage of the 59th Street Bridge used in Godfrey's office is from the opposite side of the river to the footage used for the outdoor scenes at "The Dump".
When Cornelia and Faithful George return to the scavenger hunt at the Waldorf Ritz, Cornelia addresses Godfrey by name, even though she had not actually learned it by that point in the film.
Godfrey is placing roses in a vase while ignoring Irene. In one shot, he has already placed five stems in the vase. The camera cuts away to the rest of the cast, but when Godfrey is seen again, there is only one rose in the vase.
In the living room scene just after the PARK AVENUE CHATTER column that appears, Cornelia's magazine changes. At first, Cornelia picks up a magazine having a dark stripe along the top and bottom of the front cover, then the magazine has a lighter front cover and a woman (resembling her) in an ad on the back cover. As Cornelia moves over to the couch, the magazine changes back to the original one; further, it reveals a star shape on the front cover and a non-portrait on the back cover.
At the Tea Party, while Irene is talking to Charlie Van Rumple, Godfrey is in the background with a tray serving Cornelia and she takes an item in each hand. A few seconds later, the scene shifts to Cornelia, and Godfrey again serves her, and she again takes the two items.
When Godfrey is washing the dishes, they're not being rinsed. So soap residue would still be on the plates no matter how hard Irene wipes.
When Godfrey is washing dishes because Molly "has a cold" and Irene joins him in wiping, he only washes supper plates. For one meal, there would not be so many plates used; other items should have been washed after about nine plates at most, which would include the servants' used plates.