It seems that if the nccmath package is included, then the text in the following minipage overlaps with the text before that if the minipage contains only display math. The \FixMinipageForNccmath macros is from nccmath affecting minipage widths.
\documentclass[fleqn,preview=false]{standalone}%
%
\usepackage{amsmath}%
\usepackage{nccmath}% Needed for fleqn environment
\newcommand*{\FixMinipageForNccmath}{\hrule height 0pt width \hsize}%
\begin{document}
Some text: $2 \ln x = 1$
\begin{minipage}{0.70\linewidth}\FixMinipageForNccmath
\begin{align*}
\ln x &= \frac{1}{2}
\end{align*}
\end{minipage}
\begin{minipage}{0.30\linewidth}\FixMinipageForNccmath
Note: abcd
\end{minipage}
\end{document}
\hrulehas no influence, as you probably have already noticed. – egreg Jul 2 '11 at 19:44\newcommand*{\FixMinipageForNccmath}{\leavevmode}both of the recent problems get fixed. I don't quite understand what other impacts this would have but got the idea from this recent question about aligning minipages – Peter Grill Jul 2 '11 at 20:14