Many of existing analytical studies of the IEEE 802.15.4 medium access control (MAC) protocol are not adequate because they are often based on assumptions such as homogeneous traffic and ideal carrier sensing, which are far from reality for multi-hop networks, particularly in the presence of mobility. In this paper, a new generalized analysis of the unslotted IEEE 802.15.4 MAC is presented. The analysis considers the effects induced by heterogeneous traffic due to multi-hop routing and different traffic generation patterns among the nodes of the network and the hidden terminals due to reduced carrier-sensing capabilities. The complex relation between MAC and routing protocols is modeled, and novel results on this interaction are derived. For various network configurations, conditions under which routing decisions based on packet loss probability or delay lead to an unbalanced distribution of the traffic load across multi-hop paths are studied. It is shown that these routing decisions tend to direct traffic toward nodes with high packet generation rates, with potential catastrophic effects for the node's energy consumption. It is concluded that heterogeneous traffic and limited carrier-sensing range play an essential role on the performance and that routing should account for the presence of dominant nodes to balance the traffic distribution across the network.