Load-altering attacks targetting a large number of IoT-based high-wattage devices (e.g., smart electric vehicle charging stations) can lead to serious disruptions of power grid operations. In this work, we aim to uncover spatiotemporal characteristics of LAAs that can lead to serious impact. The problem is challenging since existing protection measures such as $N-1$ security ensures that the power grid is naturally resilient to load changes. Thus, strategically injected load perturbations that lead to network failure can be regarded as \emph{rare events}. To this end, we adopt a rare-event sampling approach to uncover LAAs distributed temporally and spatially across the power network. The key advantage of this sampling method is the ability of sampling efficiently from multi-modal conditional distributions with disconnected support. Furthermore, we systematically compare the impacts of static (one-time manipulation of demand) and dynamic (attack over multiple time periods) LAAs. We perform extensive simulations using benchmark IEEE test simulations. The results show (i) the superiority and the need for rare-event sampling in the context of uncovering LAAs as compared to other sampling methodologies, (ii) statistical analysis of attack characteristics and impacts of static and dynamic LAAs, and (iii) cascade sizes (due to LAA) for different network sizes and load conditions.