This paper studies some of the fundamental challenges and opportunities associated with the network-layer broadcast and multicast in a multihop multirate wireless mesh network (WMN). In particular, we focus on exploiting the ability of nodes to perform link-layer broadcasts at different rates (with correspondingly different coverage areas). We first show how, in the broadcast wireless medium, the available capacity at a mesh node for a multicast transmission is not just a function of the aggregate pre-existing traffic load of other interfering nodes, but intricately coupled to the actual (sender, receiver) set and the link-layer rate of each individual transmission. We then present and study four alternative heuristic strategies for computing a broadcast tree that not only factors in a flow's traffic rate but also exploits the wireless broadcast advantage (WBA). Finally, we demonstrate how our insights can be extended to multicast routing in a WMN, and present results that show how a tree-formation algorithm that combines contention awareness with transmission rate diversity can significantly increase the total amount of admissible multicast traffic load in a WMN.