Mediation - or models where an intervening variable is thought to propagate an affect from a cause to an outcome of interest - is a ubiquitous statistical tool in the behavioral and medical sciences. Despite a long history of thoughtful critiques of its use in applied research, mediation remains inferentially attractive and easy to implement in widely-available software. Here we highlight a challenge of mediation that has not yet received appropriate consideration - namely the potential for improper causal inferences when the mediator is a derived, or composite, score of a set of items or measures (e.g., sums, means, differences, etc.). We show that composites have the potential to confound or mask different causal processes that occur at the individual item level, leading to spurious mediation effects. As composite measures are near-universal in many fields from the psychological to biomedical sciences, this limitation of inferences potentially impacts a very broad set of research questions. In this paper we demonstrate this issue in a diversity of mediators, using both empirical examples of grey matter volume and depression questionnaires and a wide array of simulated examples. Additionally, we provide several potential analytical approaches with may help diagnose spurious mediation with composite measures and provide greater insight into the causal structure of our data. As part of this set of approaches, we advocate a transition from traditional, regression-based approaches to mediation towards a structural equation modeling (SEM) framework which provides many advantages. We also note additional conditions under which interrupted mediation can occur, providing directions for future developments in this area.