The father's toupee looks different from scene to scene.
The Arcadia military medals that they wear in this movie are actually U.S.A.
At least one of the medals worn by the King is a US Armed Forces Bronze Star medal with star.
Several if not the majority of the medals worn by Whitaker, King Coventry and the Duke of Sterling at their public appearances are actually medals awarded for service in the Armed Forces of the United States.
Lila is seen hand-carving part of a wooden leg, with the piece resting on her knee. She is also looking away while digging into the piece. You don't have to be an expert of any kind to know how ridiculous and dangerous this is.
Anyone who restores carousel horses should know that painting in temperatures below 40 degrees almost always results in poor adhesion of the paint, resulting in a sub par paint job. And since the Thomas Carousel Restoration Company has been in business for a long time, Roy and Lily should know they should not be painting outside.
At the end of the movie, while inspecting the carousel, how is it that Lila can wear a strapless red evening dress, without either a coat or jacket, whilst it is still snowing outside.