! LaTeX Error: Not in outer par mode.

documentclass{article}
usepackage[utf8]{inputenc}
usepackage{amssymb, amsmath}
usepackage{errata}

begin{document}
begin{align*}
     erratumReplace{typo}{$a_{10}$}{$a_{00}$} &=  2 cdot 6 + (-1)cdot 4cdot 1 = 8\
         a_{10} &=  -(18 - 4) = -14\
         a_{20} &=  (3 -2) = 1\
         ||A||&= 1cdot 8 + 0cdot (-14)+ 5cdot 1 =13;.
end{align*}

end{document}

usepackage{marginnote}
makeatletter
newcommand{erratumMathReplace}[4][]{% keyvals, explanation, old, new
setkeys{erratum}{#1}stepcounter{erratum}record@erratum{#2}%
marginnote{Err(arabic{erratum})}immediatetypeout{Erratum!}%
[#4]_r^{arabic{erratum}}%
gdeferratumMath@new{#2}%
gdeferratumMath@old{#3}}
newcommand{erratumMathPrint}{%
footnotetext[value{erratum}]{text{{scshape{Erratum!}}%
@ifundefined{erratum@type}{}{(erratum@type)} (erratumMath@new) (original text was: ``(erratumMath@old)'')}}}
makeatother

documentclass{article}
usepackage[utf8]{inputenc}
usepackage{amssymb, amsmath}
usepackage{errata}

usepackage{marginnote}
makeatletter
newcommand{erratumMathReplace}[4][]{% keyvals, explanation, old, new
setkeys{erratum}{#1}stepcounter{erratum}record@erratum{#2}%
marginnote{Err(arabic{erratum})}immediatetypeout{Erratum!}%
[#4]_r^{arabic{erratum}}%
gdeferratumMath@new{#2}%
gdeferratumMath@old{#3}}
newcommand{erratumMathPrint}{%
footnotetext[value{erratum}]{text{{scshape{Erratum!}}%
@ifundefined{erratum@type}{}{(erratum@type)} (erratumMath@new) (original text was: ``(erratumMath@old)'')}}}
makeatother

begin{document}
begin{align*}% Note that the arguments to erratumMathReplace don't go inside $$
     erratumMathReplace{typo}{a_{10}}{a_{00}} &=  2 cdot 6 + (-1)cdot 4cdot 1 = 8\
         a_{10} &=  -(18 - 4) = -14\
         a_{20} &=  (3 -2) = 1\
         ||A||&= 1cdot 8 + 0cdot (-14)+ 5cdot 1 =13;.
end{align*}
erratumMathPrint% Printing the footnote
end{document}

documentclass{article}
usepackage[utf8]{inputenc}
usepackage{amssymb, amsmath}
usepackage[show]{errata}
usepackage{marginnote,xpatch}

xpatchcmd{erratumAdd}{marginpar}{marginnote}{}{}
xpatchcmd{erratumDelete}{marginpar}{marginnote}{}{}
xpatchcmd{erratumReplace}{marginpar}{marginnote}{}{}
xpatchcmd{erratum}{marginpar}{marginnote}{}{}
xpatchcmd{enderratum}{marginpar}{marginnote}{}{}

newcommand{matherratumAdd}[3][]{%
  mbox{erratumAdd[#1]{#2}{ensuremath{#3}}}%
}
newcommand{matherratumDelete}[3][]{%
  mbox{erratumDelete[#1]{#2}{ensuremath{#3}}}%
}
newcommand{matherratumReplace}[4][]{%
  mbox{erratumReplace[#1]{#2}{ensuremath{#3}}{ensuremath{#4}}}%
}

begin{document}
begin{align*}
matherratumReplace{typo}{a_{10}}{a_{00}} &=  2 cdot 6 + (-1)cdot 4cdot 1 = 8\
         a_{10} &=  -(18 - 4) = -14\
         a_{20} &=  (3 -2) = 1\
         ||A||&= 1cdot 8 + 0cdot (-14)+ 5cdot 1 =13;.
end{align*}

$matherratumReplace{typo}{x}{y}$

$matherratumAdd{typo}{a}$

erratumAdd{x}{y}

clearpage

PrintErrata

end{document}