After uploading my game save onto a new server, I get the error "ERROR: Unbound Factory Building: factory-2@Nauvis(1,310)" any time I try and enter a factory. I think the machines in them have stopped working as well. Any thoughts on what is causing this?

No idea what could cause this. Try picking them up, but don't place them down again, instead put the items away somewhere, then use the /give-lost-factory-buildings command to get backup items for all your factory buildings. Please report back if this does not solve the problem.