The most obvious conflict is the imperfection of man. Lennie is slow-witted and has a phyical strength that he does not comprehend. Consequently his like of "pretty, soft things," frequently creates problems. That's why they left their last job, and that's what leads to the eventual destruction of Lennie. The imperfection of man is also shown through Candy and his dog. Candy's dog is old and "good for nothing." Candy is badgered to let Slim put the old dog out of its "misery." Eventually, Candy gives in, and one cannot help but notice the resolution to this conflict is paralleled later by George.
Curley's wife and Curley's jealousy create conflict for all the men on the farm. She is a known flirt, and creates conflict through her flirtatious actions. Curley finds Lennie to be an easy target of his rage, but Lennie crushes Curley's hand in a physical confrontation. Later Lennie accidentally kills a puppy that had been given to him, and he eventually accidently kills Curley's wife. George knows the best and kindest thing to do for Lennie is to put him down before the others get a hold of him.
All of these events leads to another conflict and that is the destruction of hopes and dreams. All that George valued--the sense of family he got from his relationship with Lennie, operating his own ranch with Lennie and Curley--came to an end.