When using a supertabular in a multicols env. starting somewhere on a page following e.g. a section and spanning several pages the 1st page columns are filled but all subsequent page columns are only filled partially. The MWE shows this when adding a large amount of rows in the supertabular environment. A subsequent use of multicols with supertabular works ok. It seems supertabular "remembers" the left over page space when it initially starts. I had a look at the supertabular/multicols code, thinking about changing the \TrickSupertabularIntoMulticols trick code (e.g. resetting page size at \mcnewpage), but without success. It is far beyond my limited latex programming capabilities. Any ideas on how to resolve this? MWE below.
%!TEX TS-program = xelatex
%!TEX encoding = UTF-8
\documentclass[a4paper, 12pt, twoside, openright]{book}
\usepackage[left=2cm,right=2cm,top=2cm,bottom=3cm]{geometry}
\usepackage{multicol,showframe,supertabular,ifthen}
\makeatletter
\let\mcnewpage=\newpage
\newcommand{\TrickSupertabularIntoMulticols}{%
\renewcommand\newpage{%
\if@firstcolumn%
\hrule width\linewidth height0pt%
\columnbreak%
\else%
\mcnewpage%
\fi%
}%
}
\makeatother
\begin{document}
\chapter{A}
\section{a1}
\section{a2}
\section{a3}
\section{a4}
\begin{multicols*}{2}
\TrickSupertabularIntoMulticols
\begin{supertabular}{lll}
Aaaa & 0010 & text \tabularnewline
Aaaa & 0010 & text \tabularnewline
\end{supertabular}
\end{multicols*}
\end{document}

supertabularthat usually overestimates the row heights. – egreg Feb 28 '15 at 17:51