I think that Steinbeck uses dialogue as a way to flesh out the characters of Lennie and George. Right off the bat in the first chapter of the novel, the reader gets a perfect feel of Lennie's vulnerability, his loves, and his embrace of a world that is definitely not the world in front of both Lennie and George. Additionally, it is evident that George bears responsibility for Lennie. Dialogue is critical in bringing this out into full bloom. This is also seen in the third chapter of the book when George talks with Slim. Their discussion takes on a "confessional" tone, something that Steinbeck himself invokes in describing how George explains their relationship and how he looks out for Lennie. The conversation reveals how George feels responsible for Lennie and how the loyalty both men share to one another is unique for the ranching world. Slim brings this out in his measured comments, as well. Dialogue that triggers flashbacks with commentary is also a part of this process and part of Steinbeck's style:
The focus on time, too, is limited to the present: there are no flashbacks to events in the past, and the reader only learns about what has happened to Lennie and George before the novel's beginning through dialogue between the characters.
Steinbeck's use of dialogue is what enables the reader to grasp the characterization being advanced throughout the course of the novel.