How would the story have been different if Jim was the narrator in The Adventures of Huckleberry Finn? Would you trust Jim's narration?
The dialect portions of the book would obviously have been more dominant, so the reader would have had to adjust to that. And the perspective would have been quite different. Jim's main concern is that he wants to be a free man, this is completely different than Huck's desire to be "free" in the sense that he simply wants to figure his own way out in the world and avoid the traps of both his father and the widow as he works out his own path.
Jim on the other hand is actually seeking freedom from bondage and the ability to live a life not determined legally by an "owner." Regardless of the fact that his owner is relatively humane, the idea of freedom is a very different one for him and would change the story completely because of that different perspective.
Jim is also portrayed as more superstitious than Huck, so that would be a more ever-present facet of the story. Also, as the previous post says, a great deal more of the story would be about hiding and the constant worry of being caught and returned in chains and the possibility of being sold to a different owner and a completely different life.
I agree with the above post as well that there is certainly no reason to distrust Jim as a narrator, given that he is generally as honest as Huck and as trustworthy. Both of them have a certain objective and bias in telling their stories so it is different than an omniscient narrator, but I would consider his voice as trustworthy as Huck's.
It would have been quite a bit harder for the story to be as complex as it is if Jim had been the narrator. This is because Jim is a runaway slave. He clearly would not have been able to go and have all the experiences that Huck did (as with the Grangerfords and with the Wilks sisters). He would have had to remain in hiding.
As to whether he would be trustworthy, there is no reason he should be less trustworthy than Huck is. Jim is at least as good a person as Huck and so he seems to have no more reason to lie than Huck does.