E-Check (emissions testing) was just recently discontinued in the majority of Ohio, I think it may still be in place in the Northern Ohio (Cleveland) area though.
The only other thing that I can think of is you will need an 'out of state inspection' performed. It is a certificate that you will need to obtain in order to register the car in Ohio. Basically all they do is verify the vin number/odometer reading and a basic safety inspection. Our local State Highway Patrol offers this service.