I googled "public school safety inspection form" and came up with a few hits. In general, you'll need to find out what tasks they and their contractor's perform and then determine their level of compliance. You could have an excellent checklist but most of it may be blank because the school is new performs very few hazardous tasks.

MikeCJ

I think that there would be quit a few hazardous items to look for. 

Janitorial department – Here will be many hazardous chemicals, msds, training, labeling, PPE and Bloodborne pathogen training and supplies

Shop rooms – Machine guarding, PPE, training, first aid training

Maintenance – Machine guarding, Haz com, pool chemicals, PPE, electrical

Educators – Bloodborne, First aid

Transportation – Machine guarding. PPE, haz com

Of course then look at general conditions, floor condition, walls, ceilings, emergency action plan, bomb threat, civil disturbance

These are things off the top of my head, there are probably many more.

Hope this helps.