We know that having all your domains interlinked hurts Google rankings, we know that Google looks at domain registration information, hosting, etc when figuring out where to rank a site. My question is: what other shared factors do you believe Google looks for when ranking a site? E.G. Shared database connections? Similar CSS files? Other "fingerprints" in the way the code is written? Using the same functions on each site?
IP range would be, if it has same IP range its not good because they would think its a spam move creating network of blogs to manipulate links.
There are new cases and findings that google could able to get through database of a server that has more than 1 site, and able to index content into other site. Here's an example.. http://www.google.com/support/forum/p/Webmasters/thread?tid=77c605450b6db491&hl=en
Cross linking between websites hosted under the same IP may hurt you but not all the cases. If you link between relevant websites with no spam linking pattern then it would be no problem for it. For on-page factors. Just using the similar theme won't hurt you or a thousands of website using default Wordpress theme should got penalized already. The same content is worst and easiest to identify spam pattern.
I can tell you what bad backlinks are. They are links placed in footer and blogrolls. Google learned how to identify such links long time ago so try not to get such links. Don't waste time. Google also doesn't like cloacking, links from spammed pages as well as links from banned domains, links from signatures at forums in some way. There are many bad factors regarding domain itself. For example if some website hasn't any links from good websites and has only links to bad resourses, such situation could be describes as a bad one.
Good point, I hadn't thought of that. Google basically ignores the design anyway doesn't it and focuses on the content and links.
When there is a group of websites and each one is giving link to each other, then it is known as link farming, which is a black hat SEO technique. So, beware of linking several domains like this. your website might get black listed.