What is considered inappropriate dress code wise, on average? For instance, nose piercings, tattoos, and red hair. How are these viewed by employers? Will these attributes make me unhireable?
Knowing who is hiring you is key. Some older women are a lot more traditional than others. I remember in elementary school my AP had a tongue piercing and I thought she was the coolest person ever! As long as you are dressed as a professional you will be treated like one. Hair color, and small piercings and harmless in this profession. With tattoos, I would check with your employer and ask how they should be taken care of or covered.
I agree that it is based on who is hiring you. This is the best solution.
I would say, for an interview, that no facial piercings or visible tattoos should be a dominating portion of your presence. On an interview you can ask their policies on these things but I would say a more minimalist approach would be better for hire-ability.
Appropriate clothing- for men: dress slacks, a button-up shirt and tie or for women: a dress/ business suit, dress slacks, blouse and cardigan. I would not have any facial piercings in, would try to cover any tattoos to the best of my ability and would ask what the policies are once in the interview for nose piercings and visible tattoos. Dyed hair is not typically frowned upon but for an interview I would say a more natural color would be better.