Plan Recognition is the problem of inferring the goals and plans of an agent given a set of observations. In Multi-Agent Plan Recognition (MAPR) the task is extended to inferring the goals and plans of multiple agents. Previous MAPR approaches have largely focused on recognizing team structures and behaviors, given perfect and complete observations of the actions of individual agents. However, in many real-world applications of MAPR, observations are unreliable or missing; they are often over properties of the world rather than actions; and the observations that are made may not be explainable by the agents' goals and plans. Moreover, the actions of the agents could be durative or concurrent. In this paper, we address the problem of MAPR with temporal actions and with observations that can be unreliable, missing orunexplainable. To this end, we propose a multi-step compilation technique that enables the use of AI planning for the computation of the posterior probabilities of the possible goals. In addition, we propose a set of novel benchmarks that enable a standard evaluation of solutions that address the MAPR problem with temporal actions and such observations. We present results of an experimental evaluation on this set of benchmarks, using several temporal and diverse planners.