The main "gotcha" is the Federal GFSZ law... and I can see there may be efforts to strengthen it in the wake of Newtown.
Whether a state allows LOC/UOC or not, federal law requires firearms to be unloaded in a locked container or locked mount (gun rack) when within 1000ft of a K12 school.
There is an exemption for those who possess a CCW/CHL/CWP... but the exemption ONLY applies in the state of issuance.
Having a Florida non-resident CCW permits one to carry concealed in some 20+ states, but it only provides an exemption to the Federal GFSZ law in Florida.
Likewise, Arizona, Vermont, and Alaska constitutional carry laws do not provide the exemption without the CHL.
Thankfully, it is a federal law, and I've never heard of it being enforced by local authorities other than incident to arrest on other charges. Even cases where people have been arrested under California 626.9 (California's own GFSZ law), they have not been charged under the Federal statutes.
As for carrying on school property, it depends on the state. California may be tough to obtain a CCW in many counties, but it does provide an exemption and allows loaded concealed carry pretty much anywhere except a bar or courthouse.
BUT... when the gun is not on the person, the same laws that apply to a non-permitted person apply to the permitted person. If he leaves his handgun in his car, it must be in a secure locking container and unloaded.