I can offer background l that may help you contextualize this phrase. I can't say with certainty that there was not such a trend but, if so, it had no impact on First Amendment jurisprudence.

We're talking about the unanimous opinion in Schenck v. United States, authored by Justice Holmes. This was a case about whether expressing opposition to the draft was protected by the First Amendment. The Supreme Court held that it was not.

Holmes' comment on shouting, "Fire!" in a crowded theater was an illustrative analogy as to an instance when speech could constitute a "clear and present danger".

It's important to realize that this was not a scenario before the Court, nor did the Court rule on whether such speech is, in fact, protected. Nor has the Court ever ruled on a similar set of facts.

The comment is what's known as dicta, which can influence lower courts and indicate how the opinion's author's would rule in such a circumstance. It is not precedent--lower courts are not bound by dicta, only by the case's actual holdings.

In short, this phrase was an analogy, not reflective of actual events, nor binding on courts.

Not sure if you can categorise it as a big problem, but there was certainly an instance with loss of life. From the official online history of Sadler's Wells in London (http://www.sadlerswells.com/about-us/history/complete-history):

"There was tragedy, however; on October 15th, 1807 when a drunken brawl was eagerly heralded by onlookers with a joyous "A fight! A fight!". Those elsewhere in the theatre mistook the hubbub for 'A fire! A fire!" and in the ensuing stampede, eighteen people lost their lives. The root cause of the accident was alcoholic excess but this did not deter anybody connected with Sadler's Wells, according to a writer of the 1820s."

Other source for this: 'Sadler's Wells', in Survey of London: Volume 47, Northern Clerkenwell and Pentonville, ed. Philip Temple (London, 2008), pp. 140-164. British History Online http://www.british-history.ac.uk/survey-london/vol47/pp140-164 [accessed 13 June 2016].

Not quite a theater in the sense you might expect, but there was an incident in 1913 at Italian Hall in Calumet, MI. On Christmas Eve, several union mine employees and their families (about 400 people at the time of the incident) were having a party on the second floor when somebody falsely yelled about a fire in the building. Because the second-floor room could only be easily accessed by a single staircase, though there was a fire escape and some ladders leading down from windows, the crowd rushed for the exit and 73 people were killed trying to get out.

There is no definitive evidence of who called "Fire!" but there is strong suspicion by local historians and labor historians that the offender was an anti-union representative or affiliate of the Calumet and Hecla Mining Company who several eyewitnesses claim was wearing a button for the Citizens' Alliance (a major anti-union organization around that time).

The Upper Peninsula has a strong history of mining (copper, specifically, in that part of the UP) and a number of mine labor disputes played out over the early part of the 20th century, though most of the mines in the Copper Country have now been closed for decades.

Italian Hall itself is no longer standing, having been demolished in the 1980s, but the main archway for the door is still there along with a historical marker on an otherwise empty lot. The historical marker upholds a long-standing idea that the doors of the building opened inwards, contributing to the crowding, but architectural records and local newspaper accounts describe the building as having outward-opening doors.

SOURCES:

I am not myself a historian in any academic sense (so I apologize if I'm overstepping), but I lived in the area for several years and heard the story too many times to count. That said, I am aware of the following reading:

• Death's Door: The Truth Behind Michigan's Largest Mass Murder by Steve Lehto - This book is specifically about this incident.

• Hollowed Ground by Larry Lankton - Lankton was a professor at nearby Michigan Tech who taught the course History of the Copper Country. This book was the text used by that class, and it covers history at the three major mines in the area, of which C&H was one.