We have multiple thermostats in our building and someone keeps setting one to heat while leaving the other 3 thermostats on cool. Is this bad for the air conditioning system?

It all depends on how the system is zoned. This would have to be seen first hand to know if it could create a problem or not.

That's the good thing about zoning systems. You can have 1 system to satisfy multiple areas, heat or cool. Its made for climate control in each area. Its not bad for the equipment if all safety's are in place that help protect the equipment. In a office or a 2 or 3 story home it is not uncommon for it to switch back and forth from heat to cool in mild weather.