Cool tool but I'm really confused by the name choice. Sure choosing names is hard but by using a name of a common tool for an unrelated tool will just cause problems for people looking for bash spellcheck tools.
I'm the author! Since naming the tool, I've discovered that a significant segment of the population (such as yourself) repeatedly misread the name as "spellcheck".
The name is actually "shellcheck" (shell + check).
It's a fascinating effect because people seem to be very consistent in whether they read it one way or the other. If linguists don't already have a name for this sharp, binary classification, I propose "n-Gram staining".
ShellCheck already checks for bashism if the script is declared with #!/bin/sh, and finds most of the ones that checkbashisms does along with a few others. It's geared towards POSIX compliance though, and doesn't know which non-POSIX feature are available in e.g. busybox sh.
There is also some limited support for warning about features not available between non-POSIX shells, such as trying to use zsh =(temp files) in bash or bash ;;& case continuations in zsh, but this isn't as much of a focus as POSIX checks since it's not a common source of issues.
The Wooledge pitfall list was the original implementation checklist. About 38 out of the 46 are already covered in one form or another.
I haven't heard of Firehose before, but if you want to use it right now you can run shellcheck with -f gcc, to get gcc style error messages that Firehose can already parse.
The way the human brain works is crazy. You take the very very strong expectation of reading "spellcheck", and then you swap out a "p" for something that looks a lot like an upside-down "p"...and it refuses to read it as anything else.