While the string of successes found in using heuristic, best-first search methods have provided positive reinforcement for continuing work along these lines, fundamental problems arise when handling objectives whose value does not change with search operations. An extreme case of this occurs when handling the objective of generating a temporal plan with short makespan. Typically used heuristic search methods assume strictly positive edge costs for their guarantees on completeness and optimality, while the usual ``fattening'' and ``advance time'' steps of heuristic search for temporal planning have the potential of resulting in ``g-value plateaus''. In this paper we point out some underlying difficulties with using modern heuristic search methods when operating over g-value plateaus and discuss how the presence of these problems contributes to the poor performance of heuristic search planners. To further illustrate this, we show empirical results on recent benchmarks using a planner made with makespan optimization in mind.