Can I introduce a special environment which will reappear at the end?

Minimal changes from my answer at Collect the input of all \TODO commands used in the document at the end. I called the stuff "cross-refs" only because that was a tag in your question. You can call it whatever you want.

MACRO VERSION See later for environment version.

\documentclass{article}
\usepackage{ifthen}
\newcounter{crossrefindex}
\setcounter{crossrefindex}{0}
\newcommand\CROSSREF[1]{%
  \addtocounter{crossrefindex}{1}%
  \expandafter\def\csname crossref\roman{crossrefindex}\endcsname{#1}%
  #1%
}
\newcounter{index}
\newcommand\showCROSSREFs{%
  \vspace{5ex}%
  \rule{10ex}{.5ex}CROSS-REF LIST\rule{10ex}{.5ex}\\%
  \setcounter{index}{0}%
  \whiledo{\value{index} < \value{crossrefindex}}{%
    \addtocounter{index}{1}%
    \arabic{index}):  \csname crossref\roman{index}\endcsname\\%
  }%
}
\begin{document}

I start hear \CROSSREF{Fix this bug} and do some work.

Then I do thiis \CROSSREF{Get spelling fixed, too} which I have to get back
to

and then I am done

\showCROSSREFs

\end{document}

ENVIRONMENT VERSION

Unfortunately, this eats spaces after the environment, and so one must add an explicit {} after the environment if one wants to preserve it.

\documentclass{article}
\usepackage{ifthen,environ,etoolbox}
\newcounter{crossrefindex}
\setcounter{crossrefindex}{0}
\makeatletter
\NewEnviron{CROSSREF}{%
  \addtocounter{crossrefindex}{1}%
  \expandafter\xdef\csname crossref\romannumeral\value{crossrefindex}\endcsname{%
  \expandonce{\BODY}}%
  \BODY%
}
\makeatother
\newcounter{index}
\newcommand\showCROSSREFs{%
  \vspace{5ex}%
  \rule{10ex}{.5ex}CROSS-REF LIST\rule{10ex}{.5ex}\\%
  \setcounter{index}{0}%
  \whiledo{\value{index} < \value{crossrefindex}}{%
    \addtocounter{index}{1}%
    \arabic{index}):  \csname crossref\romannumeral\value{index}\endcsname\\%
  }%
}
\begin{document}

I start hear \begin{CROSSREF}Fix this bug\end{CROSSREF}{} and do some work.

Then I do thiis \begin{CROSSREF}Get spelling fixed, too\end{CROSSREF}{} which I have to get back
to

and then I am done

\showCROSSREFs

\end{document}

Several variations are possible, but here's a start.

\documentclass{article}
\usepackage{environ}

\usepackage{lipsum} % just for the example

\newcounter{repeatatend}
\makeatletter
\def\repeat@at@end{} % initialize

\NewEnviron{important}{%
  \par
  \medskip
  \BODY\par
  \medskip
  \refstepcounter{repeatatend}%
  \label{repeatatend@\romannumeral\value{repeatatend}}%
  \xdef\repeat@at@end{%
    \unexpanded\expandafter{\repeat@at@end}%
    \unexpanded{\noindent(p.~\pageref}{repeatatend@\romannumeral\value{repeatatend}}) %
    \unexpanded\expandafter{\BODY\par}%
  }%
}
\AtEndDocument{\section*{Important}\repeat@at@end}

\begin{document}

Here I state something very important
\begin{important}
\textbf{Lorem Ipsum Principle.} Blah blah blah.
\end{important}

\lipsum % to get to another page

Then another important thing
\begin{important}
Ducks can fly.
\end{important}
which is something to take into account.

And then I am done.

\end{document}

Here's the relevant part at page 1

Here's what happens at the end