Some other people are saying they've seen Chrome complain, but I can't reproduce it. Please send email (support@pinboard.in) if you can figure out what's up.
Cert chain is incorrect basically and the browser is fetching intermediate certs to try to make it work.
Most of the issues Qualys points out on blog.pinboard.in are not present on pinboard.in itself, so I presume there's a difference in config there that would be a good place to start. They're also running on different versions of Debian (squeeze v. wheezy, which ship different OpenSSLs) which accounts for some of the variance.
Also, as Qualys notes, disable RC4 ciphers on pinboard.in and you're in pretty good shape.