Other mistake: When Josey confronts the Comancheros, the Chief notes that they are facing the sun. You can see that the sun is on the back of all the characters who are looking at Josey...meaning Josey is the only one looking into the sun.
Other mistake: When Josey, Lone Watie, and the Indian woman stop in a town, Josey listens to the General store clerk who hands him a postcard that shows "Slim Fixin" after he was killed. The postcard is actually a real life photograph of gunfighter/outlaw Bill Doolin after he was gunned down.
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