Context: LaTeX is a typesetting system. When compiling a document, a lot of really in-depth debugging information is printed, which can be borderline incomprehensible to anyone but LaTeX experts. It can also be a visual hindrance when looking for important information like errors.
Thank you for this writeup, very informative. I get a lot of these "badness 10000" messages when working with things that have "complex" layouts, for example a resume/CV template. Given that TeX was originally made for research papers/articles, it makes sense that weirdness would arise when it's used for more layout-heavy stuff!
Badness 10000 usually indicates that something is very wrong. Usually overfull hboxes. If the text is spaced out to the point where it immediately looks bad, that could still be like badness 5000. What I have seen mostly is macros not playing well with other macros, and in LaTeX there's a lot of macros under the hood, so it's very hard to troubleshoot.