Revealing mistake: Following their escape from the comancheros, the two wheeled wagon driven by the old woman had a set of reins coming through the slats beneath the seat indicating that the old lady held fake reins and the wagon/horses were controlled by someone inside. Later, when they left the small town and headed to her son's ranch, a little window had been cut out of the slats where the control reins came through, no doubt to improve visibility and horse control.
Revealing mistake: When Josey returns to the tent and discovers that Jamie has died, you can see the 'dead' Jamie blink his right eye.
Answer: At first, the story advances very rapidly, essentially giving the audience a primer lesson on Josey's angry motivation; so, many minute details aren't explored, such as where he acquired his ammunition. We might conjecture that Josey had a separate out-building, called a "powder house" (which was common in that era) where gunpowder and shot was kept for safety reasons. If he did, that raises the question of why the raiders didn't ransack and burn his powder house as well.
Charles Austin Miller