Hi there,
Sam from Moz's Help Team here - sorry for any confusion!
So, something to note here is that unlike the rest of the metrics available in Open Site Explorer, the Spam Score doesn't update each month with the rest of the index update. The Spam Analysis section updates on a completely separate schedule, and much less frequently; usually around every 6 months or so. So it's entirely possible that you're seeing Spam flags that are no longer relevant to your site.
It's always best to trust your instincts: for example, if you know you've got contact info on the site, and we're flagging you for it being missing, you can safely ignore that warning.
The spam score also is not based solely on backlinks.
I'd recommend checking out this article & video that our co-founder Rand wrote on our Spam Analysis tool (they're absolutely the best way I've found to understand this metric) — but I'll also be happy to add some key takeaways from these resources, as well.
Article: Spam Score: Moz's New Metric to Measure Penalization Risk
Video: Understanding and Applying Moz's Spam Score Metric - Whiteboard Friday
Essentially, Spam Score is an aggregate of 17 different flags we set up to identify traits that correlate with measured Google penalization. The higher the number of flags on a link, the higher the chance that it's spammy.
The flags represent a wide variety of potential signals ranging from content concerns to low authority metrics. Since this is just based on correlation with penalization, rather than causation, the solution isn't necessarily to change these factors on your site, but it could be worthwhile to consider them!
I hope this helps answer your questions around the Spam Analysis tool, as well as how to decipher what the scores mean. If not, or if there's anything else I'm able to assist with, please don't hesitate to ask!