As long as the new site does not have the same content problems, google will take no notice of the redirect. The reason they don't take notice is, imagine of I had a grudge against someone or was competing against their site. I could very easily register a domain with the contact details of the competing site. Then purposely get it banned from google. Redirecting this site to my competitor would then get them dropped by google.
That said, it would still be a black mark against the site, and would be counted in that respect. As long as it is not the only source of traffic for the new domain, you shuold be OK. I would, however, advise you to get the new domain listed in google before doing the redirect, and to ensure that it has some good, safe incoming links.
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Coop
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