In answer to the original question, the answer is yes. The Theater is responsible for the safety of the movie goers.
This is not to say that they have strict liability, and are liable if anything whatsoever happens to the patrons. But, when a business owner invites the public onto its premises, for the purpose of benefiting the business owner, the law imposes one of the highest duties of care upon the owner for the safety of the public. (The patrons are, under law, "invitees.") Though the standards vary somewhat from state to state, the owner owes a duty to anticipate all reasonably foreseeable accidents and injuries on the premises, whether from physical conditions or other patrons, and to take affirmative steps to prevent those accidents and injuries.
If a mass shooting is reasonably foreseeable in a movies theater in todays society, then the theater must provide safety mechanisms to prevent it.
One of the first modern cases in this area involved the teen singer in the early 1960s (Connie Frances.) She checked into a Holiday Inn, and then was raped went she went out into the walkway to get ice. She sued the hotel, claiming that since they had invited her to stay there, then they had a duty to provide reasonable security. The hotel claimed no, that they simply provided a limited service of a room for the night, with no assurance of safety. The Court ruled in favor of Connie big time, stating that she was a business invitee on the premises, and that as such, the hotel had a duty to provide reasonable security. Since the hotel had provided absolutely none, they were hit with a big judgment and had to pay out the nose to Connie.
Of course Connie was never the same again after that assault. Though she had enjoyed a big string of teen hits prior to that night, I don't think she ever had a successful song again.
Mannyrock
