Should be overturned?! This guy was making multiple threats to multiple people, why should that be protected on the Internet? Personally, he was rightfully convicted and similar action should be taken to anyone making violent threats online. Making violent threats is not, in my opinion, an exercise in free speech. Or, put another way, there are consequences to what a person says, such as falsely crying fire in a theater or making a threat against a person.
All courts agree that "true threats" are not protected by the First Amendment but that "rhetorical hyperbole" is protected (e.g., a poster on FR who says "Obama is a traitor and should be hanged.")
The issue before SCOTUS--and one that has split the lower courts-- is whether the jury should be instructed that it had to find that the defendant intended to threaten the victim, or whether it is enough that the victim reasonably believed that she has been threatened. (In other words, in deciding whether something is a "true threat" or "rhetorical hyperbole," do you look at it subjectively and from the defendant's perspective, or objectively and from the victim's perspective.)
Here, the victims all testified that they felt threatened, but the defendant claimed he was just "blowing off steam." (The jury probably wouldn't have believed him anyway, but they were instructed that his intent didn't matter.)