Factual error: Clem puts the paper photo into an envelope and licks the flap to seal it. Paper photographs didn't exist in the 1880s (photos were still tin-types). Pre-cut, pre-gummed envelopes, though they'd been invented, were big-city luxuries rare-to-non-existent in the "wild" west - they were too expensive for most people (like Clem) to afford, especially in the economically depressed decades following the Civil War. You generally cut and folded your own envelopes and glued or sealing-waxed them shut.
Continuity mistake: Heyes and Curry both lose their hats when they jump from the riverboat into the water and swim ashore. There's no time to go back and fish the hats out, even if they could find them, but by the next episode and for the rest of the season, they somehow have the same hats back again.
Other mistake: When Doc Donovan reads the wanted posters, the physical description of Heyes mentions dark brown hair and brown eyes, which fits Pete Duel. However, by this episode, Roger Davis had taken over the role. He has light brown hair and blue eyes.