Why do I get this error in this very simple mwe?

You need to insert a paragraph break before the chapter line. As \par directly is not allowed, use \endgraf:

\documentclass[notoc]{tufte-book}
\setcounter{secnumdepth}{3}
\setcounter{tocdepth}{3}

\begin{document}

\tableofcontents
\chapter{Introduction}

\startcontents[chapters]
\printcontents[chapters]{}{1}{}

\section{Historical Overview}
\section{The CUDA Model}
\section{A Lattice Boltzmann Solver}

\addtocontents{toc}{text\endgraf}

\chapter{chap3}
\section{My Overview}
\end{document}

It stems from the introduction of random text inside the .toc file via

\addtocontents{toc}{text}

If you wish to do so, ensure that the text is on its own by issuing a \par afterwards.

The following minimal example replicates the problem:

\documentclass{article}

\begin{document}

\tableofcontents

\section{A section}

\addcontents{toc}{text}% Error
%\addtocontents{toc}{text\par}% No error

\section{Another section}

\end{document}