Standpoint linear temporal logic (SLTL) is a recently introduced extension of linear temporal logic (LTL) with standpoint modalities. Intuitively, these modalities allow to express that, from agent a’s standpoint, it is conceivable that a given formula holds. Besides the standard interpretation of the standpoint modalities, we introduce four new semantics, which differ in the information an agent can extract from the history. We provide a general model checking algorithm applicable to SLTL under any of the five semantics. Further we analyze the computational complexity of the corresponding model checking problems, obtaining PSPACE-completeness in three cases, which stands in contrast to the known EXPSPACE-completeness of the SLTL satisfiability problem.