Today I found out, that it is not possible to use the normal \footnote{This is a footnote} command inside a math environment.

To solve the problem the command \footnotemark has to be used where the little number should occur and the command \footnotetext{This is a footnote} right after the environment has been closed.

Example:

\begin{align*}
 SPL & = 20 \log \dfrac{p_{rms}}{p_{ref}}, \qquad
 p_{ref} = 2 \times \unit[10^{-5}]{Pa}\footnotemark
\end{align*}
\footnotetext{Believed to be the threshold of hearing
(at \unit[1]{kHz}) at the beginning of the 20th century, 
however it turned out that this value is somewhat to low.}