This is not legal advice; were this to be legal advice, a bill for services would be attached.
Now that that's out of the way... Here's a 30 second analysis of how a sign can become a bludgeon.
An argument can be made that the rules for entry posted in the signs are a unilateral contract for entry. Why would a contract for entry be necessary? Absent permission to enter, noone has permission to enter the land of another - and such permission can be conditioned upon certain events. For premises held open to the public - such as malls - most people on that property are considered invitees. Other types of people on property not their own are Licensees and Trespassers. A Licensee, according to Blacks (7th Ed, 1999), is "(2) One who has permission to enter or use another's premises, but only for one's own purposes and not for the occupier's benefit." One with a mere license is tolerated on the property but not asked to leave (e.g. taking a shortcut across a neighbor's property), invited to enter (Invitees), or have passibe consent. A Tresspassor is "one who intentionally and without consent or privilege enters another property. There is tortious tresspass and criminal tresspass - the former does not require police intervention or a prosecution.
How does that interact with signage? It can be argued that the signs provide the "ground rules" (the unilateral contract for permission to enter) by which the occupier of the property grants a license, or invites, the public onto its property. VA Code 18.2-119 begins thus: "If any person without authority of law
goes upon or remains upon the lands...." (Emphasis mine.) A licensee or invitee has authority of law to enter, thus is not a tresspassor.
OK, so that took me about 10 minutes, mostly looking up the specific definitions.
Remember: this is not legal advice. I am not your attorney, nor am I offering to become your attorney.