Here's a few of the biggest concerns, at least from what I've read about from people's experiences living near existing ones.

• Water usage (can drain local groundwater, drive up water prices)
• Power usage (can drive up electricity prices, burns more fossil fuels or shifts clean energy to itself making other people now reliant on fossil fuels)
• Noise (people even at fairly large distances away can often still hear the sounds from the datacenter, it never stops and runs 24/7, can often give people nonstop headaches)
• Pollution (many datacenters have generators they can use, and they pollute the local air. Even if not run regularly as part of primary operations, many datacenters do tests anywhere from every month to every year to make sure the generators and backup systems work as intended, can suddenly generate a lot of air pollution without warning)

And that's not to mention secondary effects, like how it can do things like draw in crowds of temporary workers that then incentivizes short term rentals (i.e. Airbnb's) in the local area over actual homeowners, and can drive up housing costs, or how it can attract local subsidies that would otherwise go to smaller businesses that actually really need it.