The Wall Street Journal Law Blog reports on this question, and quoting Prof. Fred Schauer (a leading First Amendment scholar), our coblogger Stuart Benjamin, and me. The relevant statute makes it a crime to “knowing the information reported, conveyed or circulated to be false or baseless,” “circulate a false report or warning of an alleged occurrence or impending occurrence of a crime, catastrophe or emergency under circumstances in which it is not unlikely that public alarm or inconvenience will result.” For the tweets that might lead to a prosecution of @ComfortablySmug, see here.
As to the War of the Worlds question flagged at the end of the WSJ post, see 47 C.F.R. § 73.1217:
No licensee or permittee of any broadcast station shall broadcast false information concerning a crime or a catastrophe if:
(a) The licensee knows this information is false;
(b) It is forseeable that broadcast of the information will cause substantial public harm, and
(c) Broadcast of the information does in fact directly cause substantial public harm.
Any programming accompanied by a disclaimer will be presumed not to pose foreseeable harm if the disclaimer clearly characterizes the program as a fiction and is presented in a way that is reasonable under the circumstances.
Note: For purposes of this rule, “public harm” must begin immediately, and cause direct and actual damage to property or to the health or safety of the general public, or diversion of law enforcement or other public health and safety authorities from their duties. The public harm will be deemed foreseeable if the licensee could expect with a significant degree of certainty that public harm would occur. A “crime” is any act or omission that makes the offender subject to criminal punishment by law. A “catastrophe” is a disaster or imminent disaster involving violent or sudden event affecting the public.