This is an accurate portrayal of events.
The movie begins in 1795. Up until the mid-19th century, firearms were almost entirely muzzle-loading, which John's musket clearly is. So, given that it had taken an experienced soldier some 20-30 seconds to load a musket (even longer to load a muzzle-loading rifle) and being in a situation where he hadn't cleared the area of hostiles, John dropped his musket after firing it once and quickly grabbed his first back-up weapon -- in this case, a pistol that he was carrying on his left hip.
Incidentally, if he'd needed to shoot his pistol, which was also muzzle-loading, his second back-up weapon was a knife that he was carrying on his right hip.
The movie begins in 1795. Up until the mid-19th century, firearms were almost entirely muzzle-loading, which John's musket clearly is. So, given that it had taken an experienced soldier some 20-30 seconds to load a musket (even longer to load a muzzle-loading rifle) and being in a situation where he hadn't cleared the area of hostiles, John dropped his musket after firing it once and quickly grabbed his first back-up weapon -- in this case, a pistol that he was carrying on his left hip.
Incidentally, if he'd needed to shoot his pistol, which was also muzzle-loading, his second back-up weapon was a knife that he was carrying on his right hip.
In the opening sequence, when Beecham shoots at the bandit who is attacking the young woman, he fires a rifle. But when he then comes down to the coach to check on the travelers, he is holding a pistol.
The lead character is riding a horse in the beginning but the saddle is not correct for 1795.
About 34:34 in, one can see on the floor a bit of orange marker tape where the actors are meant to meet.