Problem grouping environments

Question

Below are two examples. The first one works fine, no errors no warnings, but on trying to build a doc from the latter, I get a heap of errors.

Working:

\documentclass[]{article}
\usepackage{environ}

\newsavebox{\DiscardedText}
\newcommand{\Slide}[1]{}
\newcommand{\SavedSlideText}{}
\newcommand\AddToSavedSlideText[1]{\xdef\SavedSlideText{\SavedSlideText#1\endgraf}}
\NewEnviron{GobbleExceptForSlide}{%
    \renewcommand{\Slide}[1]{\AddToSavedSlideText{##1}}%
    \savebox{\DiscardedText}{\BODY}%
    \SavedSlideText%
}

\AtBeginDocument{\GobbleExceptForSlide}
\AtEndDocument{\endGobbleExceptForSlide}

\begin{document}

Should not show in output

\Slide{Should show in output}

\end{document}

But if I put an itemize either below or into the Slide command, then it fails with Paragraph ended before \@savebox was complete \end{document}:

\Slide{

Should show in output

\begin{itemize}
 \item Item one
 \item Iten two
\end{itemize}

}

I'm tried replacing the 'newcommand' with 'newenvironment' and related changes, but I could not get that to work either. I'm a little rusty...

Update

The answer provided below does solve part of the problem, but for some reason it breaks when using an environment outside the Slide. The following tex won't compile, because there is an itemize environment outside of the Slide.

\documentclass{article}
\usepackage{environ}

\makeatletter
\newsavebox{\DiscardedText}
\newcommand{\Slide}[1]{}
\newcommand{\SavedSlideText}{}
\newcommand\AddToSavedSlideText[1]{\g@addto@macro\SavedSlideText{{#1}}}
\NewEnviron{GobbleExceptForSlide}{%
    \renewcommand{\Slide}[1]{\AddToSavedSlideText{##1}}%
    \savebox{\DiscardedText}{\BODY}%
    \SavedSlideText%
}
\makeatother

\AtBeginDocument{\GobbleExceptForSlide}
\AtEndDocument{\endGobbleExceptForSlide}

\begin{document}

Should not show in output

\begin{itemize}
 \item Item one
 \item Iten two
\end{itemize}

\Slide{
Should show in output

   \begin{itemize}
    \item Item one
    \item Iten two
   \end{itemize}
}

\end{document}

Answer 1

Update Based on revised MWE.

Unfortunately I don't know why this problem occurs. But, one way to proceed is to eliminate the warning of missing list items as per How to make itemize/enumerate/description environment robust to missing \item elements?

Code: Suppress Missing Item Error

\documentclass{article}
\usepackage{environ}

%% Allow for lists to have no items.
%% https://tex.stackexchange.com/questions/86547/how-to-make-itemize-enumerate-description-environment-robust-to-missing-item-el
\makeatletter
  \let\@oldnoitemerr\@noitemerr %Save the command definition                      
  \newcommand\IgnoreMissingItemError{\let\@noitemerr\relax}
  \newcommand\DontIgnoreMissingItemError{\let\@noitemerr\@oldnoitemerr}

\newsavebox{\DiscardedText}
\newcommand{\Slide}[1]{#1}
\newcommand{\SavedSlideText}{}
\newcommand\AddToSavedSlideText[1]{\g@addto@macro\SavedSlideText{{#1}}}
\NewEnviron{GobbleExceptForSlide}{%
    \renewcommand{\Slide}[1]{\AddToSavedSlideText{##1}}%
    \savebox{\DiscardedText}{\IgnoreMissingItemError\BODY}%
    \SavedSlideText%
}
\makeatother

\AtBeginDocument{\GobbleExceptForSlide}
\AtEndDocument{\endGobbleExceptForSlide}

\begin{document}

Should not show in output

\begin{itemize}
 \item Item one
 \item Iten two
\end{itemize}

\Slide{
Should show in output

   \begin{itemize}
    \item Item one
    \item Iten two
   \end{itemize}
}
\end{document}

---

An alternate approach is to typeset the document and save the \Slide content for output that content at the end of the document.

Code: Generate all content, and Slide content at end

\documentclass{article}
\usepackage{environ}

\makeatletter
\newcommand{\Slide}[1]{#1}
\newcommand{\SavedSlideText}{}
\newcommand\AddToSavedSlideText[1]{\g@addto@macro\SavedSlideText{{#1}}}
\NewEnviron{GobbleExceptForSlide}{%
    \renewcommand{\Slide}[1]{\AddToSavedSlideText{##1}##1}%
    \BODY%
}
\makeatother

\AtBeginDocument{\GobbleExceptForSlide}
\AtEndDocument{\endGobbleExceptForSlide\clearpage\SavedSlideText}

\begin{document}

\section{foo}

Should not show in output

\begin{itemize}
 \item Item one
 \item Iten two
\end{itemize}

\Slide{
Should show in output

   \begin{itemize}
    \item Item one
    \item Itenn two
   \end{itemize}
}
\end{document}

---

In your previous question Is there a way to display a specific command and hide the rest, there was no information as to the type of content that the \Slide macro would have. So, as David Carlisle suggested you need to use an alternate solution from How keep a running list of strings and then process them one at a time to save the content:

Code:

\documentclass{article}
\usepackage{environ}

\makeatletter
\newsavebox{\DiscardedText}
\newcommand{\Slide}[1]{}
\newcommand{\SavedSlideText}{}
\newcommand\AddToSavedSlideText[1]{\g@addto@macro\SavedSlideText{{#1}}}
\NewEnviron{GobbleExceptForSlide}{%
    \renewcommand{\Slide}[1]{\AddToSavedSlideText{##1}}%
    \savebox{\DiscardedText}{\BODY}%
    \SavedSlideText%
}
\makeatother

\AtBeginDocument{\GobbleExceptForSlide}
\AtEndDocument{\endGobbleExceptForSlide}

\begin{document}

Should not show in output

\Slide{
Should show in output

\begin{itemize}
 \item Item one
 \item Iten two
\end{itemize}

}
\end{document}