After Emil Peck accosts Kitty and Doc, Matt shows up while Kitty is buggy-whipping him. Matt doesn't have his hat with him, but a couple seconds later it's in his hands while he's telling Peck he'll go to jail if he doesn't stay out of trouble.
When Matt and Jennings are talking the morning after they catch up to Mady, Jennings's shadow is very pronounced on Matt's chest, making the sun behind Jennings. When Little Bear arrives, Matt turns completely around, which should put the sun behind him. But there is a shadow coming from Matt's right, 90 degrees from where the sun should be.
At the 8:53 mark, the scene cuts to the flag at Fort Dodge. The flag has 35 stars, but the 35-star flag was only in use during the Civil War from 1863, when West Virginia was admitted to the Union, to 1865 when Nevada joined.
Going by dates seen on tombstones on Boot Hill, the timeframe is somewhere around 1883 and later. The correct flag for the period from 1876 to 1890 had 38 stars.
Kitty and Doc are on the way to Delmonico's for dinner. After Kitty gets knocked into the horse trough, in the time it takes her to change, get made up, and get to Delmonico's, Mrs. Arthur goes to the army fort, talks to the colonel for a little while, gets back to Dodge and has a conversation with Matt. It would have taken her a while by buggy to get to and from the fort.