When using \bm, I can't use \dot and \hat on uppercases A-F (lowercases and the rest of the alphabet are fine), and it instead writes the Gamma character, along with an error message the the value input to \bm was to high.
\documentclass{article}
\usepackage{amsmath}
\usepackage{bm}
%this is just the layout of the "table"
\newcommand{\layer}[2]{&&\dot #1&&\hat #1&&\widehat #1&&&\dot #2&&\hat #2&&\widehat #2\\&\bm{#1}&&\bm{\dot #1}&&\bm{\hat #1}&&\bm{\widehat #1}&&\bm{#2}&&\bm{\dot #2}&&\bm{\hat #2}&&\bm{\widehat #2}\\}
\begin{document}
\begin{equation}
\begin{aligned}
\layer{a}{A}\\
\layer{b}{B}\\
\layer{c}{C}\\
\layer{d}{D}\\
\layer{e}{E}\\
\layer{f}{F}\\
\layer{g}{G}
\end{aligned}
\end{equation}
\end{document}
And the console says
\layer{a}{A}
\\
A mathchar number must be between 0 and 32767.
I changed this one to zero.
and similar for the other letters B-F.

\bmuses different fonts than normal. Not all of them are complete. See also Knuth's poor man's boldface.