For example, carrying a gun (open or concealed) in an air carrier terminal (even on the dirty side of security, is illegal.
Incorrect.
There was a minor effort at making it so after the doofus wandered around Atlanta-Hartsfield with his AR one day, but there is no Federal law currently on the books that prohibits firearm carry in "the dirty side" of airports, air carrier or no.
The "patchwork" of State law as you mention, is usually the thing that will trip people up. Some airports are considered to be "local government buildings" and then fall into local law regarding sign postings, trespass law if requested to leave, etc.
There's also the stuff that's made to resemble law/authority which has no legal standing in some places, like the aforementioned signage.
The devil is in the details. Take Denver International for an example...
- Transporting: Carrying a cased unloaded firearm into the terminal to check it as baggage in a locked case, 100% legal. Most airlines will also require that ammunition not be locked in the same case as the firearm. See specific airline's rules.
- Non-secured non-TSA areas of the airport are posted as no firearms. These signs carry zero weight of law in Colorado but do serve to confuse the public in general. They also serve to notify legal firearms carriers that the most likely action if one is noticed carrying a firearm is a call to police who will arrive, harass, and ask the property owner or representative what they want someone carrying to do. The answer is of course, "to leave". If one refused to do so, it would be a misdemeanor trespassing charge and of course, an escort off of the property.
- DIA being within the City and County of Denver, also falls within the legal confines of Denver's "Assault" Weapons Ban as well as Denver's ban on open carry, which is blatantly unconstitutional under the State Constitution and a 2003 law passed to preempt local law with State law, but Denver found judges willing to legislate from the bench, and the split 3:3 decision means the answer has never been truly settled. However currently this is interpreted as meaning Denver City and County can keep their bans.
- If one argues that DIA is a "government building", prohibiting carry of a firearm may only be done when all entrances to the building/facility are secured (metal detectors at all entrances) and by State Law such buildings must provide adequate safe gun storage for firearms to be checked in at the security checkpoint. If no security checkpoint to check all entrants is provided, the building may not prohibit firearms carry. (Numerous public facilities break this law and either attempt to post the non-legally binding signage instead, or simply refuse to offer the required safe storage. Various exclusions to the public building laws exist for specific events. DIA is not included in those specific exclusions.)
There's more but as you can see, the local laws just are a mess. And you're guaranteed to be harassed if spotted.