Jim Smiley is pretty much the main character in this story. I would say that he is what my grandparents used to call a "character." In other words, he's kind of eccentric.
His main characteristic seems to be that he really loves to bet. He loves to bet so much that he will, for example, even go out and find a frog for the stranger so that Jim's own frog can have someone else to compete against.
He's also kind of silly. I think we see this in how he names his animals after famous people like Andrew Jackson and Daniel Webster.
Jim Smiley was a man who was hopelessly addicted to gambling. He placed bets compulsively, but he also invested in gambling seriously as his occupation. He would bet on just about any random event if he had someone to bet against him, and in those cases he wasn't picky about which side he was on. If the person who was available to bet didn't like the side he was being asked to bet on, Smiley would switch sides in order to get him to bet. He would bet on how long it would take "a straddle bug" to get to wherever it was going, and he'd bet on which of two birds sitting on a fence would fly away first. Probably the most pertinent example to show his compulsive betting is that when he heard that the parson's wife would recover from her sickness, he stated without thinking, "Well, I'll resk [sic] two-and-a-half she don't anyway."
Smiley was not content to place bets randomly, however. He acquired and trained various animals to perform in contests which he would then take bets on. In particular, he would win bets with animals that didn't look like they were competitive but would surprise in the end. He had a "fifteen-minute nag" that was slow and had asthma but would always win its races by a neck. Smiley also had a bull-pup that didn't look like much but had a special way of holding onto the other dog's hind legs that would win every time—until it was pitted against a dog with no hind legs.
He put special effort into his frog, Dan'l Webster, training it for three months to be the best jumper. He also trained it to catch flies on command. So Smiley wasn't just a random gambler—he put effort into choosing and training his animals.
Obviously, as a gambler, Smiley's biggest fault was being reckless. He was so excited about having a stranger bet with him against his frog that he left Dan'l Webster alone with the stranger while he went to catch a frog for the stranger to use in the contest. Not expecting the stranger to cheat, he ended up losing the bet. One could consider him naive or gullible in that sense, but his actions are more likely explained by his excitement for gambling that makes him lose his common sense at times.