True, but I'm not sure how much Jane really cares about his public credibility. Also, he's solved about 200 cases and is generally known as a "case closer", plus the guy he killed was proven to be a psycho. Annd, people might think this is one of Red John's men copy-catting his style and not the actual Red John.
And no, as far as I'm aware there's nothing in the past about a Blinking Red Light. Most episode titles involve red somehow, but I don't think most of them are actually relevant in a deep way.