First, I want to point out that I am licensed in North Carolina, whose laws may be somewhat different than those in Ohio. With that being said, I believe you could have an argument that you should not be disqualified for unemployment benefits. If you were performing your job to the best of your ability and you feel like a lack of training and/or ability is what caused the mistakes, then that should not disqualify you. Of course, as with most legal issues, the best argument doesn't always win. I think it would be beneficial for you to consult with a local attorney familiar with unemployment hearings. I believe that would drastically help you chances of being successful.
You're not saying whether it was an initial determination, or a denial by a hearing officer. If it was an initial determination, you can appeal to have a hearing before a hearing officer. It sounds like you were let go for just cause, due to mistakes which you acknowledge. If you decide to appeal, you might want to focus on the conditions of your job that may have caused you to make mistakes. And if your mistakes were all first time only mistakes, you might want to argue that the third criteria wasn't met, that your employer's expectations weren't reasonable. From what you've presented however, I think an appeal would be a longshot, but hopefully for your sake I'm proven wrong.
Your best bet is to consult and attorney who specializes in employment law.
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