Martin Splitt from Google said on the latest SEO office hours that having lots of nofollow or noindex tags or attributes on your site does not signal to Google that you have quality issues with your site or many low quality pages.
The question was, "Can using a lot of nofollow or noindex tags signal to Google that the site has many low-quality pages?"
Martin Splitt said, "No." "It doesn't signal low-quality content to us," he added.
Martin said, "It just tells us that you have links that you're not willing to be associated with, or you have pages that you don't want to end up in the index."
Then Martin explained why it might be normal for a site to use a lot of nofollow link attributes. He said:
That can have many different reasons for the links, for instance, because they are user generated content. In which case you could tell us that they are real UGC instead of nofollow or you don't know what these sites that you're linking to will be doing in a couple of years or so, so you mark them as nofollow, that's not a problem.
And for the noindex tag he said:
If you have pages that you don't want in the index that can have lots of reasons to and there's nothing wrong with marking them noindex if you don't want them in the index.
This came up at the 1 minute and 18 second mark into this video:
Forum discussion at YouTube.