If the main body of a script executed via nsIJetpack.evalScript() throws an exception that isn't caught, it isn't reported as an error via a "core:exception" message. Looking at the source code, it seems like this is a result of the JSOPTION_DONT_REPORT_UNCAUGHT option being set on the context running JS in the Jetpack child process and the fact that JetpackChild::RecvEvalScript() isn't checking the return value of JS_EvaluateUCScript() and calling JS_ReportPendingException() if it's failed. I could be wrong, though. This bug also has a workaround, in that the whole script that's executed can just be surrounded by a try ... catch.
Comparing JetpackChild::RecvEvalScript with JetpackActorCommon::RecvMessage (which *does* throw an exception) it seems as if it is enough to just check the return value of JS_EvaluateUCScript and call JS_ReportPendingException, as Atul suggested. I have tried this out and it looks as if this does indeed solve the problem.