Some creative use of enumitem:
\documentclass{article}
\usepackage{enumitem}
\newcounter{itemcount}
\newenvironment{countitemize}[1]
{\def\countitemizelabel{#1}%
\setcounter{itemcount}{0}%
\itemize[label=\stepcounter{itemcount}\textbullet]}
{\addtocounter{itemcount}{-1}%
\refstepcounter{itemcount}\label{\countitemizelabel}%
\enditemize}
\begin{document}
Here are the \ref{mylist} points I wanted to address:
\begin{countitemize}{mylist}
\item important issue;
\item another important issue;
\item oh, and yet another critical thing.
\end{countitemize}
Let's check the formatting
\begin{itemize}
\item important issue;
\item another important issue;
\item oh, and yet another critical thing.
\end{itemize}
\end{document}

If you want to count every instance of \item, then you can do
\documentclass{article}
\usepackage{etoolbox}
\newcounter{itemcount}
\newenvironment{countitemize}[1]
{\def\countitemizelabel{#1}%
\setcounter{itemcount}{0}%
\preto\item{\stepcounter{itemcount}}
\itemize}
{\addtocounter{itemcount}{-1}%
\refstepcounter{itemcount}\label{\countitemizelabel}%
\enditemize}
\begin{document}
Here are the \ref{mylist} points I wanted to address:
\begin{countitemize}{mylist}
\item important issue;
\item another important issue;
\item oh, and yet another critical thing.
\end{countitemize}
Let's check the formatting
\begin{itemize}
\item important issue;
\item another important issue;
\item oh, and yet another critical thing.
\end{itemize}
\end{document}
However, the counting would go on in nested environments. It would be possible to solve the issue, in case you need it.
I provide for nested countitemize up to level 3.
\documentclass{article}
\usepackage{etoolbox}
\newcounter{itemcounti}
\newcounter{itemcountii}
\newcounter{itemcountiii}
\makeatletter
\newif\ifnestedcountitemize
\newenvironment{countitemize}[1]
{\ifnestedcountitemize\else
\preto\item{\stepcounter{itemcount\romannumeral\@listdepth}}%
\nestedcountitemizetrue
\fi
\begin{itemize}%
\def\countitemizelabel{#1}%
\setcounter{itemcount\romannumeral\@listdepth}{0}}
{\addtocounter{itemcount\romannumeral\@listdepth}{-1}%
\refstepcounter{itemcount\romannumeral\@listdepth}\label{\countitemizelabel}%
\end{itemize}}
\makeatother
\begin{document}
Here are the \ref{mylist} points I wanted to address:
\begin{countitemize}{mylist}
\item important issue;
\item another important issue;
\item oh, and yet another critical thing.
\begin{countitemize}{innerlist}
\item With a nested list
\item again
\end{countitemize}
\end{countitemize}
There is an inner list with \ref{innerlist} items.
\end{document}

itemizedoes not use a counter really,\label(and it's at the wrong position anyway) is useless here. Do you really want to have anitemizeor rather anenumeratelist? – Feb 26 '16 at 13:24