I'm pretty humble about what I know. That said, it sometimes pays to not undersell (when others are confidently wrong, and there's no time to explain why, for example).

I'm not so much talking about humility that you communicate to other people but about actually thinking that the other person might be right.

I don't see what "integral over many possibilities" has to do with consistency, except that it's sometimes the correct (but more expensive) thing to do.

There are cases where the forward backward algorithm gives you a path that's impossible to happen. I would call those paths inconsistent.

That's one of the lessons I learned in bioinformatics. Having a algorithm that robust to error is often much better than just picking the explanation that most likely to explain the data.

A map of the world that allows for some inconsistency is more robust than one where one error leads to a lot of bad updates to make the map consistent with the error.