i don’t think there’s a straightforward way for regular users to do this. it’s easy enough to find verifiable observations that meet the “two thirds” rule, since you can filter for research grade in the Explore page. so then for the rest of this post, let’s focus on how to do something similar for just non-verifiable (aka casual) observations…
community taxon is complicated to calculate on your own. number of agreements and disagreements don’t always mean what you would expect them to mean in every context. however, the iNat API observation search endpoint does provide each observation’s community id, which you can compare against the observation taxon. the endpoint also provides many options for filtering. besides the obvious parameters, there’s a identifications=some_agree/most_agree parameter (not available in the Explore page, as far as i can tell) which will effectively help to filter cases where there at least 2 identifications (in this use case). so for non-verifiable records at a species level, filtering with that parameter will get you really close to your intended result, and the Obs taxon = Community taxon comparison will get you the rest of the way.
it’s not super straightforward to parse through the response from this endpoint without some coding. so if you’re not a coder, you can use a page that i made to present the results in a human-friendly format. use the option below whose parameters look closer to what you prefer (captive only vs any casual), and then look for cases where the value in the Obs Taxon = Community Taxon column is true.
… and here’s another variation that might be useful (casual + research grade, with an extra column that displays photo URLs):