MikeNoLastName: You may be confusing one problem for another. I don't think the redirect from domain.com to www.domain.com is going to cause any problems. However, the permanent redirect to newdomain.com (assuming newdomain.com is really a brand new, just registered domain) is probably going to cause problems with the so-called 'sandbox' problem.
The sandbox problem prevents new sites from ranking for their terms, even though the site may be in the index. Your permanent redirect is essentially saying "dont go do olddomain.com/page.htm anymore, since it's moved permanently to newdomain.com/page.htm". Google removes oldomain.com/page.htm from the index, spiders newdomain.com/page.htm, and then puts it in the sandbox.
Matt Cutts had said at one of the conferences that Googlebot can follow multiple redirects fairly well, as long as they aren't four or five levels deep. I think you've got the sandbox working against you.