Now I actually want
a story about a time-traveling murderer, and the clever people who finally stop him or her. I mean, there are all sorts of reasons that one might go back into the past to kill someone, but why would a person want to kill someone from hundreds of years in his future? Unless he was just a psychopath looking for the perfect crime, but that is much less interesting.
Also, how much do I love Ryan's answer that a time-traveling murderer wouldn't have rusty bullets (sorry, "lead balls"), because they would be new? THIS MUCH.
Amusingly, I have a "time travel" tag, but can't use it at this moment, since that would also constitute a spoiler.