When Kar climbs through Jade's window as it changes to the inside shot it looks like a different window to the outside shot, the appearance of the window sill is not the same and Kar is also grabbing the inside ledge not the outside ledge as before.
When Nina talks to the captured Nameless Monk, she shows him two newspaper clippings. The leftmost clipping, titled 'Unknown Asian Man Saves Three Children' has the lyrics to Sunscreen as the body text below the author's name.
At the inside shot of Kar climbing through Jade's window when he lets go with his hands he appears to be quite well supported, even though the previous outside shot showed there was nothing for him stand on outside.
When the Monk is teaching Kar fighting moves, he holds Kar down and Kar has his right hand on the Monk's right shoulder. Kar's hand goes from being flat, and angling up to grasping the Monk's shoulder as the angle of the shot changes from looking at the Monk to looking at Kar.