When John is leaving for Europe, in the wide shots of the ship leaving the dock, two different ships are shown, although they have a similar paint scheme.
When Mary goes riding and is thrown from her horse, the horse that runs off after she falls is a different one than the one she jumped over the wall and fell from. Note the two white lower rear legs on the horse running off after the fall. Also, the saddles are different from when she first got on the horse, to the jump/fall scene, to the horse running away after.
When Dr. Monica reads the note from Mary the hand shown holding the note has nail polish on, whereas Kay Francis wasn't wearing nail polish.
When Mary flies her plane from New York City towards Paris, the sun is on the horizon as the plane flies over the Atlantic Ocean. However, she took off in the afternoon or evening before sunset, so the only way the sun could be on the eastern horizon would be if it was the next morning. However, the mechanic said the plane only had two hours of fuel. Also, Anna called Monica before midnight about Mary's plane being lost.
After John and Monica get out of the canoe, they lie under a tree to watch the sunset. But even though the sun is supposed to be in front of them and low in the sky, there's sunlight coming through the trees from above and behind them.