I am able to answer this question specifically as it pertains to first amendment protections within the United States, going back much further and into different countries, you're of course going to have different answers. For this answer, please understand none of what I am saying is legal advice, I am a graduate of law school who just has some academic background with this specific area of first amendment law. I will also be speaking to a purely criminal background, because civil law has different standards as to what is and is not actionable speech. The government can’t jail you for defamation for example, but you could be sued for it by an injured party.

First, at a very basic level, most crimes have two core elements. Mens Rea, and Actus Reus. Guilty mind, and guilty act. That's a fancy way of saying a criminal intent and a criminal action. When considering murder, a 1st degree murder is generally one in which the defendant acted with the intent to kill the victim, and achieved that intent.

Criminalizing a threat can be understood in the same way from a legal perspective. Here is the terroristic threat statute from my home state of PA for context.

Focusing specifically on the portion as it relates to violent threats (a)(1), you'll notice it specifically criminalizes the making of a threat to commit any crime of violence (the criminal act) with the intent to terrorize another (the criminal intent). For Mulaney's joke, the police likely wouldn't take it seriously as a criminal threat, because (1) it wasn't communicated to the alleged victim in the first place, meaning no criminal act was actually committed, and (2) the following up of it with the line about improv practice would make clear to any reasonable person it was meant in jest, with all the additional context.

Understanding how this fits in with the first amendment, the case to look to for an answer, that is fairly analogous, is Watts v. United States. (1969)

(I include the full case because it's fairly short, worth reading if you're interested, although I'll summarize the main points below)

Watts was a young man in the process of being drafted into the Vietnam war. At a political rally, he said that he'd never get drafted, and that if they made him carry a rifle, the first person he'd want to get in his sights would be L.B.J. He made a gesture as if aiming down the barrel of a rifle, and the statement itself drew laughter from the crowd.

He was subsequently arrested and charged with threatening the life of the president. His case ultimately made it to the Supreme Court (I'm skipping over quite a bit of procedural history for the sake of brevity) wherein the court established a true-threat exception to the First Amendment, and held that Watts speech wasn't truly a threat, because any statement considered a threat has to be understood within context and the court must consider the purpose of hyperbole. The court drew attention to the fact that it elicited laughter from the audience and that Watts himself found the statement funny.

The court did not ultimately define clearly what a true threat was in this case, defaulting to the arguments surrounding context.

So to answer specifically the question as it pertains to legal protections, going back to 1969, Mulaney would be protected, because the context surrounding it makes it fairly clear he was not being serious.

Going back further though, you are going to run into a lot of trouble clearly nailing down what is and is not protected speech. It shouldn't be particularly surprising to know that the First Amendment speech protections have changed substantially over time. The Alien and Sedition act of 1798 wasn't formally ruled unconstitutional for example, until 1964. This act made it a federal crime to make false or malicious statements about the government, and was used to prosecute and fine individuals who were critical of the government. Matthew Lyon, a member of the House, was arrested for accusing President Adams of "an unbounded thirst for ridiculous pomp."

I also can't articulate fully the ways in which the protections of the law were selectively granted to individuals depending on factors such as racial background and political statements. Abolitionist newspapers and activists were regularly attacked in the period leading up to the civil war. One of my favorite anecdotes that a professor used to illustrate this point is that of Reverend Elijah Lovejoy. He published The Alton Observer, which was an abolitionist newspaper in Alton, Illinois. In 1837, a mob attempted to destroy his printing press and attacked the building, attempting to set it on fire. Reverend Lovejoy and some of his compatriots engaged in a shootout with the mob, resulting in his death.

A subsequent trial reached verdicts of not-guilty for everyone in the mob. There were accusations of impropriety on the part of the prosecution, the judge, and the entire legal community within the town.

I bring this up to make the point that even if your speech is legally protected, if the state isn't protecting you, it makes it difficult to ensure your safety. Cops and the legal system have been slow to change, and that change will depend entirely on where you are, who you are, and what you're saying.

If you're interested in an academic paper on the topic of legal threats specifically, I highly recommend Threats, Free Speech, and the Jurisprudence of the Federal Criminal Law, which discusses what I've summarized in a more strictly academic manner. I've included the cite for the article below.

G. R. Blakey & Brian J. Murray, Threats, Free Speech, and the Jurisprudence of the Federal Criminal Law, 2002 BYU L. Rev. 829 (2002). Available at: https://scholarship.law.nd.edu/law_faculty_scholarship/614

Mods if there are any issues with this comment let me know. It's not strictly historical, as this question called for some legal analysis.