Yes, they could affect your rankings, probably more so if you're getting errors and warnings from them, and even if you don't want to index them, depending on which kind of errors you're getting, it'd be probably a good idea to fix them up, as they will still be part of your site.
Now, if you use robots.txt those pages could get indexed anyway (i.e. someone else links to them), and could also stall ranking factors, read more here.
About the links, you'd probably be better off using 'noindex' instead of 'nofollow', to make sure pages aren't indexed and don't drain your juice, but I guess in this case the best choice would be to use a 'noindex, follow' meta tag within those pages, to make sure they aren't indexed and don't drain your site.
Although, if the content is sensitive (as you say, customer data) it'd be better to password protect it, that way you'd be blocking not only search engine bots but malicious robots, spyware, and uninvited users as well.