The Fifteen Minute Nag
The mare which is always given a head start because she’s so slow is nicknamed “The Fifteen Minute Nag.” This is the kind of low-level irony you see expressed in a bald man called “Curly” or a short person nicknamed “Stretch” because the mare always winds up being fast enough to win the race. Which is only as fast as a horse ever needs to be, of course.
East v. West
The primary irony at work in the story is that the Westerner Simon Wheeler appears to get the better of the Easterner, “Mark Twain.” The underlying tension in the tale is that Twain’s readership back East viewed frontier folk as simple, gullible and intellectually inferior to their more sophisticated Eastern cousins. That may have been true even on general principles, but in this particular case, Wheeler more than proves that either Westerners are a bit more clever or Easterners a bit less clever than advertised.
The Parson's Wife
When Smiley inquires as to the health of the Parson’s wife, the Parson responds by informing that she is getting better. The Parson is quite sincere and thankful about the turn for the better, but Smiley’s response makes the entire exchange brutally ironic since he doesn’t actually care about the Parson’s wife’s health at all and is only interested in how his reply affects the odds.
Searching for Leonidas
The whole reason that Mark Twain is there listening to the interminable tales of Jim Smiley via Simon Wheeler is because he was trying to track down this mysterious Leonidas Smiley fella. The overarching theme related to the frame story of the tale is that by the time he’s through not only has not succeeded in finding Leonidas, he has come to believe such a person does not even exist.
The Dept. of Frog Behavioral Sciences
A subtle bit of irony in the story that often flies right over the head of readers is its entire premise. According to Wheeler, Smiley does little else for three straight months over than teach the frog to jump and to catch flies. But since frogs are pretty much incapable of moving in any other way than jumping and rely upon their instinctual ability to catch pretty like flies in order to survive…why would Smiley need to spend three minutes much less three months teaching these things?