We present an on-line algorithm for the runtime checking of temporal properties, expressed as past-time Linear Temporal Logic (LTL) over the traces of observations recorded by a "black box"-like device. The recorder captures the observed values but not the precise time of their occurrences, and precise truth evaluation of a temporal logic formula cannot always be obtained. In order to handle this uncertainty, the checking algorithm is based on a three-valued semantics for pasttime LTL defined in this paper. In addition to the algorithm, the paper presents results of an evaluation that aimed to study the effects of the recording uncertainty on different kinds of temporal logic properties.