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\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[natbibapa]{apacite}
\title{For testing}
\begin{document}
Information about natbib in \citeauthor{sharelatex}.
\bibliographystyle{apacite}
\bibliography{bibli.bib}
\end{document}
This gives the error "Missing $ inserted". What has mathmode to do with apacite or citeauthor?
The problem is the _ in the url, which can normally only be used in math mode. In order to use them in a url, either use the url or the hyperref package.
\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[natbibapa]{apacite}
\usepackage{url}
\usepackage{filecontents}
\begin{filecontents*}{\jobname.bib}
@misc{sharelatex,
title={ShareLaTeX, the Online LaTeX Editor},
url={nl.sharelatex.com/learn/Natbib_citation_styles},
journal={ShareLaTeX, Online LaTeX-verwerker}
}
\end{filecontents*}
\title{For testing}
\begin{document}
Information about natbib in \citeauthor{sharelatex}.
\bibliographystyle{apacite}
\bibliography{\jobname}
\end{document}
$in yourbibli.bibfile..bibentry (e.g., underscores) could cause this. But without looking at the specify.bibentry, it's hard to tell.