(at around 35 mins) When Holmes and Rathe are fencing, Holmes drops his saber when he is cut, but in the next scene he is seen holding his saber - with no break in the dialogue to give him a chance to pick it up.
(at around 1h 30 mins) When Watson swings the grapple to hook the axle, there is a crossbeam at the rear of the buggy that the rope swings on before hooking on the axle. When the hook catches the axle and Rathe starts to drive away, the crossbeam is missing and the rope is stretched straight behind the carriage instead of upwards, the knot holding the hook has changed shape, and the axle is smooth. When the rope catches and the carriage is ripped apart, the knot has returned to its original shape, the crossbeam is still missing, and a fitting resembling an inchworm has appeared in the middle of the axle.
Holmes "chemistry experiment" could not have caused Dudley's hair to go white if Dudley had consumed it, as implied by Holmes' claim to have dropped it in Dudley's tea. Only hair grown AFTER consuming something could be affected - the existing hair would remain its original color.
None of the laced darts shot at but one of their victims are ever visible, and could not possible have travel such long distances without dropping significantly or being visible, especially when all the victims were wearing very thick winter clothing which would have been impossible to penetrate.
It is clear that Waxflatter's flying machine, regardless of the "wing being made of the wrong material", was always completely incapable of flying, not only because of faulty construction but because sustained flight at the low speed Holmes and Watson were "flying" to save Elizabeth would have been impossible because the wingspan was ridiculously short. This is also revealed during filming as being suspended by cables.
(at around 28 mins) Holmes admitted himself that Dudley had hidden the fencing trophy inside a vase of "freshly baked and painted ceramic," which, when discovered and dropped intentionally by Holmes to reveal the hidden trophy, it did not leave a trace of paint on Holmes' hand, having nowhere sufficient time to dry, let alone be painted by Dudley so shortly after firing (in the school kitchen's oven).
Considering how cold it would need to be to freeze the water or the river/lake so thick, no one's breath is visible while they are outside. Especially so during the climactic fight at the end where the body temperatures would have risen.
The artwork sketch of the six men including Cragwich, that Watson shows Holmes in the attic is a completely different drawing than the sketch they show to Elizabeth a few minutes later in the film. The two sketches are supposed to be the same sketch but the four men towards the center of the sketch look very different from one scene to the other.