Thanks for your help, Bernadette. I really appreciate your advice.
I had thought to crawl the site-- I see a few 302 redirects and one 404 response. Webmaster Tools does not indicate any errors found by Google.
The link idea is a good idea-- when I took a look at our backlinks detected by OpenSite Explorer, I find that we have increased in the number of links in the last 3 months 120 (we had lost 50 links, but the domains linking to our site overlap completely). Moz does not show any of the links as spammy.
Are there any other link-related tools that I should be considering here?