When Dmitri and Vlad are walking away from Anya in the Palace after they tell her she could be Anastasia, Dmitri is timing her on a wristwatch. This takes place in the 1920's so he wouldn't have a wristwatch, he would of had a pocket watch. Wristwatches weren't invented yet!
Actually, it is highly possible and definitely probable that he had a wrist watch. See, at first only wealthy men owned wrist watches, but during WW1, they were made for pilots, and after the war ended, evryone wanted one, so wrist watches were made affordable for people who weren't so wealthy.