The problem is not the document class, but the accented letters from Spanish (in this particular case, "ó" and "á"). The known workarounds for listings: using literate or even escaping the accented characters to LaTeX (suugested, for example, in How to insert code with accents with listings?) won't work for showexpl since non-ascii characters get lost when the temporary file internally used is written.
I'd like to suggest you the powerful tcolorbox package and its nice interaction with listings; here's a little example (adjust the settings according to your needs; in particular, you need to add support for accented uppercase vowels, the crema and the eñe):
\documentclass[twoside]{tufte-handout}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[spanish,mexico]{babel}
\usepackage[many]{tcolorbox}
\tcbuselibrary{listings}
\lstset{%
language=[LaTeX]TeX,
basicstyle=\ttfamily\small,
commentstyle=\itshape\ttfamily\small,
showspaces=false,
showstringspaces=false,
breaklines=true,
breakautoindent=true,
captionpos=t,
literate=%
{á}{{\'a}}1
{é}{{\'e}}1
{í}{{\'i}}1
{ó}{{\'o}}1
{ú}{{\'u}}1
}
\tcbset{
example/.style 2 args={
colframe=red!50!black,
colback=red!50!black!5,
fonttitle=\small\sffamily\bfseries,
fontupper=\small,
fontlower=\small,
text outside listing,
title={Ejemplo~\thetcbcounter: #1},label={#2}},
}
\newtcblisting[auto counter]{micodigo}[3][]{example={#2}{#3},#1}
\begin{document}
\begin{micodigo}{ejemplo de listas}{eje:lista}
\begin{itemize}
\item Introducción a \LaTeX
\item Texto con \LaTeX
\begin{itemize}
\item Reglas básicas
\item Entornos de texto
\begin{itemize}
\item Incisos, citaciones y poemas
\begin{itemize}
\item \textsf{quote}
\item \textsf{quotation}
\item \textsf{verse}
\end{itemize}
\item Listas
\begin{itemize}
\item \textsf{itemize}
\item \textsf{enumerate}
\item \textsf{description}
\end{itemize}
\item Texto alineado horizontalmente
\begin{itemize}
\item \textsf{flushleft}
\item \textsf{center}
\item \textsf{flushright}
\end{itemize}
\item Texto mecanografiado
\begin{itemize}
\item \textsf{verbatim}
\end{itemize}
\end{itemize}
\end{itemize}
\end{itemize}
\end{micodigo}
\end{document}
The result:

As Ignasi suggested in his comment, you can avoid the use of literate by using the listingsutf8 package. In this case, you load tcolorbox as follows:
\usepackage[many]{tcolorbox}
\tcbuselibrary{listingsutf8}
\tcbset{listing utf8=latin1}
A complete example:
\documentclass[twoside]{tufte-handout}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[spanish,mexico]{babel}
\usepackage[many]{tcolorbox}
\tcbuselibrary{listingsutf8}
\tcbset{listing utf8=latin1}
\lstset{%
language=[LaTeX]TeX,
basicstyle=\ttfamily\small,
commentstyle=\itshape\ttfamily\small,
showspaces=false,
showstringspaces=false,
breaklines=true,
breakautoindent=true,
captionpos=t,
}
\tcbset{
example/.style 2 args={
colframe=red!50!black,
colback=red!50!black!5,
fonttitle=\small\sffamily\bfseries,
fontupper=\small,
fontlower=\small,
text outside listing,
title={Ejemplo~\thetcbcounter: #1},label={#2}},
}
\newtcblisting[auto counter]{micodigo}[3][]{example={#2}{#3},#1}
\begin{document}
\begin{micodigo}{ejemplo de listas}{eje:lista}
\begin{itemize}
\item Introducción a \LaTeX
\item Texto con \LaTeX
\begin{itemize}
\item Reglas básicas
\item Entornos de texto
\begin{itemize}
\item Incisos, citaciones y poemas
\begin{itemize}
\item \textsf{quote}
\item \textsf{quotation}
\item \textsf{verse}
\end{itemize}
\item Listas
\begin{itemize}
\item \textsf{itemize}
\item \textsf{enumerate}
\item \textsf{description}
\end{itemize}
\item Texto alineado horizontalmente
\begin{itemize}
\item \textsf{flushleft}
\item \textsf{center}
\item \textsf{flushright}
\end{itemize}
\item Texto mecanografiado
\begin{itemize}
\item \textsf{verbatim}
\end{itemize}
\end{itemize}
\end{itemize}
\end{itemize}
\end{micodigo}
\end{document}
\tcbuselibrary{listingsutf8}and withoutliterate, there's no problem with accented characters. – Ignasi Jun 25 '15 at 18:09