This is an interesting question, because it isn't as straightforward as you might think. It is Twain telling the story, so in that sense, it is written in the first person point of view. He says "I" and writes the outer frame of the story from his own perspective. But then, he gets to the general store and he switches to a direct quoted dialogue by the colorful Simon Wheeler; however, the main action is not about Simon Wheeler or Mark Twain. Simon Wheeler tells the story of one Jim Smiley. So, the actual written version of this tale is almost third-hand folklore. The events happened to a Jim Smiley, as told by Simon Wheeler, as heard and re-written by Mark Twain. So, the structure and point of view of this story is very unique; I provided a link below that discusses it further.
If you are looking at the actual opinions and attitudes that come through the most, and that is what you mean by point of view, then it would have to be a 2-fold answer again. Twain's opinions and attitudes about the red-neck southern ways of the people in this town, and of Simon Wheeler, come through very strong. He is sarcastic and uses the story as a form of satire, making fun of all of the lazy southerners with no jobs who sit on main street chewing tobacco and whittling all day long. Simon Wheeler is one such type of man. So, Twain's satire and sarcastic point of view come through in the outer framework of the story. But as the tale of Jim Smiley is told by Simon Walker, you get Walker's point of view about the events, complete with his superfluous rambling backstories and colorful dialect. So the point of view in the middle, during the part about the jumping frog, is distinctly Simon Wheeler's, because he takes over telling the tale.
I hope those thoughts help; good luck!