In most existing localized topology control protocols for mobile ad hoc networks (MANETs), each node selects a few logical neighbors based on location information, and uses a small transmission range to cover those logical neighbors. Transmission range reduction conserves energy and bandwidth consumption, while still maintaining the network connectivity. However, the majority of these approaches assume a static network without mobility. In a mobile environment, however, network connectivity can be compromised by two types of "bad" location information: inconsistent information, which makes a node select too few logical neighbors, and outdated information, which makes a node use too small a transmission range. In this paper, we first demonstrate the existing problems, and then propose a mobility-sensitive topology control method that extends many existing mobility-insensitive protocols. Two mechanisms are introduced: consistent local views that avoid inconsistent information, and delay and mobility management that tolerate outdated information. The effectiveness of the proposed approach is confirmed through an extensive simulation study.