I use a number of tools in static code analysis for my projects - primarily Java based. Mostly
Wait, I hear you say. Spell checking? Absolutely, it's a key part of code and documentation quality. There's absolutely no excuse for shoddy spelling. And I sometimes find that if the spelling's off, it's a sign that concentration levels weren't what they should have been, and other errors might also have crept in.
checkstyle is far more than style, although it has very fixed ideas about that. I have a list of checks that must always pass (now I've cleaned them up at any rate), so that's now at the state where it's just looking for regressions - the remaining things it's complaining about I'm happy to ignore (or the cost of fixing them massively outweighs any benefit to fixing them).
One thing that checkstyle is keen on is thorough javadoc. Initially I might have been annoyed by some of its complaints, but then realised 2 things. First, it makes you consider whether a given API really should be public. And more generally as part of that, having to write javadoc can make you reevaluate the API you've designed, which pushes you towards improving it.
When it comes to shellcheck, I can summarise it's approach as "quote all the things". Which is fine, until it isn't and you actually want to expand a variable into its constituent words.
But even there, a big benefit again is that shellcheck makes you look at the code and think about what it's doing. Which leads to an important point - automatic fixing of reported problems will (apart from making mistakes) miss the benefit of code inspection.
Actual coding errors (or just imperfections) tend to be the domain of PMD and SpotBugs. I have a long list of exceptions for PMD, depending on each project. I'm writing applications for unix-like systems, and I really do want to write directly to stdout and stderr. If I want to shut the application down, then calling System.exit() really is the way to do it.
I've been using PMD for years, and it took a while to get the recent version 7 configured to my liking. But having run PMD against my code for so long means that a lot of the low hanging fruit had already been fixed (and early on my code was much much worse than it is now). I occasionally turn the exclusions off and see if I can improve my code, and occasionally win at this game, but it's a relatively hard slog.
So far, SpotBugs hasn't really added much. I find its output somewhat unhelpful (I do read the reports), but initial impressions are that it's finding things the other tools don't, so I need to work harder to make sense of it.