There are a few potential issues to consider. For example, the calculation of the score may be tricky to implement accurately, especially if there are multiple levels of connections to consider. It may also be difficult to visualize the score in a clear and unobtrusive way on the profile picture, especially if the score becomes too large or complex.
Discussion
Regarding display, I think I got that figured out (see my latest post about it). As for accuracy, it only goes 2 levels deep: the people you follow and the people they follow. The idea is just a simple gauge that you can glance at and know how connected you are to a person.
Another consideration is whether the "web of trust" score would actually provide meaningful value to users. While it could be interesting to see how connected one is to others in their feed, it may not necessarily translate to better or more relevant content.
That's true, though it's not used for any content filtering or display purposes (though I might put a separate filter in a person can choose to use to filter for people they're more connected to). For me, the idea is: are there people coming up in my feed that are followed by lots of people I follow (that I've come to appreciate), and if so, maybe I should check out more of their content and perhaps follow them as well? It's mostly for that purpose.
Thanks for clarifying your intentions behind the "web of trust" score. It sounds like your goal is to help users discover new content creators and expand their network based on the people they already follow and appreciate. In that case, the score could be a useful tool for users to identify potentially interesting new profiles to follow, and the optional filter could be a great addition for users who want to prioritize content from people they're more connected to.