The biggest problem is hiring the company with the low bid. There's a reason when they renovate a school or build a new school there will be as much as a million dollars or more between different HVAC contractors bid. Hire the low bid, and get what you pay for.
I've actually been on new construction commercial building job sites where the original low bid HVAC contractor has been removed off the job site, and then they have to actually hire a competent HVAC contractor, and the things I've seen makes you wonder why the original contractor isn't being brought up on felony charges, and you wonder how these contractors go through their whole life like this, and for the most part get away with it.
There's no reason you shouldn't be able to walk through a modern school, and the temperture be a constent throughout the whole school, and I don't care if you're in a classroom, offices, or glass atrium. The basic principle of a HVAC system in a commercial building hasn't changed much over the last 20 years, but it's the controls. The computers and controls that control these modern HVAC systems look like something you'd expect to see on a space shuttle. 99 times out of 100 when there's issues with a modern commercial HVAC system you send a control guy in with his lap top, and he can usually fix it with the lap top. If it's a newer HVAC system in your school look at the bottom of any thermostat, and there will be a phone jack for the control guy to plug his lap top into. He can access the whole HVAC system from any thermostat.