When disguised as chamber maids, both Mary Jack and Carla are wearing high heels. However, no chamber maid wears heels while working.
Max asks Mary Jack for a corkscrew after trying and failing to open the champagne. However, champagne - which is under pressure - doesn't require a corkscrew. Indeed, attempting to open champagne with one could result in a serious injury.
Near the end when Smart shoots the chair out of Mary Jack Armstrong's hand with his fake finger gun, he says "The old finger in the gun trick". He should have said "The old gun in the finger trick".