When Jerry goes to sprinkle sand on the floor, it is obvious from the lack of carpet pattern that there is already lots of sand on the floor.
When Jerry is driving the hansom cab to the riding academy, he tap dances on the floor of the driver's seat to get Dale's attention. The close-up of his shoes shows them to be a light color,. But a short time later when Jerry drives the cab to the gazebo, his shoes are a dark color.
During the conversation between Jerry and Horace in the bathroom, Horace's right arm is on the tub rim in shots from behind him but his right arm is in the tub in shots facing him.
When Horace and Bates are speaking to the hotel manager, the hook of the coat hanger that Bates is holding changes orientation between shots.
When Jerry and Dale are on the balcony of the hotel; the bracelet on her left hand is resting on the wrist. Jerry then proposes marriage and places his left hand on her wrist covering the bracelet. When it cuts to a reverse angle shot the bracelet is now resting just underneath her elbow although she never did anything that would cause the bracelet to slide.
When Dale and Beddini leave the hotel in London, it is obvious the drivers of the cabs are sitting on the left. The UK drives on the left, so the drivers should have been on the right.
The opening scenes shows Jerry Travers already seated in the lounge of the club. No gentlemen's club, at least a London club, to this day allows guests to be seated in the lounge before their sponsor arrives and vouches for them.
When Jerry is dancing, it appears that the main room in Horace's Suite is directly over the bedroom of the downstairs suite of Dale. Most hotels are built to an identical pattern on each floor. It is more economical that way. So for the dancing to wake Dale, Jerry should be dancing in one of the bedrooms, especially as his dancing appears to dislodge a ceiling tile in Dale's Suite.
At the gazebo, studio lights are reflected off the top of the hansom cab and the umbrella.