A formal analysis technique aiming at finding safety errors in multithreaded systems at runtime is investigated. An automatic code instrumentation procedure based on multithreaded vector clocks for generating the causal partial order on relevant state update events from a running multithreaded program is first presented. Then, by means of several examples, it is shown how this technique can be used in a formal testing environment, not only to detect, but especially to predict safety errors in multithreaded programs. The prediction process consists of rigorously analyzing other potential executions that are consistent with the causal partial order: some of these can be erroneous despite the fact that the particular observed execution is successful. The proposed technique has been implemented as part of a Java program analysis tool. A bytecode instrumentation package is used, so the Java source code of the tested programs is not necessary.