As Burko said, it does depend on other factors, but if there isn't much ventilation in the room, mold is certainly a potential problem. I know that some of my uncovered tanks and sumps have resulted in mold issues.
Many individuals can suffer from allergic reactions to mold. If it was in your home, you'd only be putting yourself at risk, but in a public space like a school you could be putting other students at risk as well. If mold does develop and is not kept under control it could pose a health risk and may require professional mold remediation. The school would probably be liable so I can see why your teacher may be hesitant about the idea.
If you're not going to have a lid, I think the best way to avoid mold issues would be to install ventillation/exhaust fans above the pond.