1) No one who is armed in school would remain secret for long. Teachers and faculty dish the gossip, kids overhear and have gossip of their own, everyone is known and seen daily. There is no way to have a long term air marshal type set of people in the school from a secrecy standpoint.
2) While concerns for non-mass murder type criminal acts (drug dealer student stealing or taking weapon and killing another student, for instance) are real in some districts, they tend to be relatively few urban and some suburban districts where there are already entry security and some amount of armed hall security in place. These districts are not likely to adopt such a policy and regardless they already run the "rip the gun away and start blasting" risk because they're probably using rent-a-cops or perhaps retired police who don't have anywhere near the kind of training that has been suggested is necessary to have a weapon in such an environment.
3) In those districts that would consider this policy, they are likely in suburban and rural areas where they do not have entry security and either have none or very limited hall security. As such the greater risk, even with faculty carrying concealed (or open carry) weapons, is that someone will come in with a weapon of their own and either commit a directed violence or mass murder type crime. Allowing responsible, law abiding adults (who are already faculty and are thus "trusted" and considered responsible) to carry is a minimal risk increase. The risk falls even lower if you require some training above and beyond mere CCW licensing.
4) On training. First, I think it is smart to leave it to the district or county to set the training requirements they deem necessary. State regulation is too wide a level for such a decision, since they will at best have to set minimum standards to meet their most crowded and problematic school districts which places unnecessary and undue burden on the vast majority of districts in a state. And what politician worth their salt stops only at the minimum requirements for a law, particularly when "the children" are involved?
That said, the state has a role to play by making non-binding recommendations, perhaps on a graduated scale for districts with different risk factors. Second, it has been suggested that something on the order of SWAT type training and testing regimens is necessary. I disagree. First, those people train for much different jobs, scenarios, and risk levels of encountering those scenarios than faculty that are maybe going to encounter such a situation in their entire lives. Second, the most likely two scenarios for faculty to encounter where they'd even consider use of deadly force are already being in the room that an assailant (armed or not) enters or encountering an assailant while guiding students out of the building. These both chuck deescalation, negotiation, room entry and clearing, and a myriad of other skills SWAT and other LEOs train for out the window. Its all about protecting kids and self, seeking cover if possible and available, knowing when to engage and when to evade, fast reaction, ensuring clear lines of fire (background and foreground and being aware of people entering the line of fire), and being accurate and controlled with shots. My feeling on this is to make training on the "immediate" scenarios annual and mandatory, encourage weekly range time but require only monthly (done on the honor system, likely verifiable after a shooting if necessary). Encourage participation in the training and policy with cost sharing schemes between trainee and the district.
5) If such policies are allowed in the state then the state should pass liability minimization laws for faculty and districts if a person under such a program is involved in a shooting. Again, these are not SWAT or even police officers. Those groups maintain high levels of liability because they train a lot and it is their job to deal with those situations day to day. Faculty and districts wanting to adopt this kind of policy, which is aimed at stopping incidents before they become worse then they already are, should be encouraged by minimizing their liability exposure. This will help keep district liability insurance to a minimum and hopefully free a faculty member under the program from having to carry their own liability insurance. Important is that this state law does not link liability minimization to any specific set of training requirements as that would just become the backdoor way of enforcing statewide minimum regs that are too stringent for the majority of districts.