Equations in the margin: automatic flush right or left?

If you do not need numbered equations, then use a simple array

\documentclass[twoside]{scrartcl}
\usepackage{amsmath}
\usepackage{lipsum}
\usepackage{marginnote}
\newenvironment{Array}
  {\arraycolsep=1.4pt\par$\array{rl}}
  {\endarray$}
\begin{document}
\lipsum[1]
\marginnote{Is flush left (manually)
  \begin{Array}
    a&=1 \\
    b&=1 
  \end{Array}}
\lipsum[2]
\marginnote{How to make flush left automatically?
  \begin{Array}
    a&=1\\
    b&=1
  \end{Array}}
\lipsum[3-6]
\marginnote{Is flush right (manually):
  \begin{Array}
    a&=1\\
    b&=1
  \end{Array}}
\lipsum[7]
\marginnote{How to make flush right automatically?
  \begin{Array}
    a&=1\\
    b&=1
  \end{Array}}
\lipsum[8-9]
\end{document}

This is what I would call semi-automatic.

The everyshi package provides a hook into the page shipout routine by means of the \EveryShipout macro. As such, the code

\usepackage{everyshi}% http://ctan.org/pkg/everyshi
\def\flusheqnL{&} \def\flusheqnR{}%
\EveryShipout{%
  \ifodd\value{page}
    \gdef\flusheqnL{} \gdef\flusheqnR{&&}%
  \else
    \gdef\flusheqnL{&} \gdef\flusheqnR{}%
  \fi
}%

defines \flusheqnL and \flusheqnR to have default values of & and {}, respectively, and alters these values based on the page number \value{page} at shipout. If the page number is odd, the values are swapped to {} and &&, respectively, to accommodate a different alignment on the following (even) page. In fact, these macros are used as hooks for alignment characters in the flalign* environment. However, this requires you to typeset your marginnote equations using the following format:

\marginnote{...
  \begin{flalign*}
    \flusheqnR ...&... \flusheqnL \\
    \flusheqnR ...&... \flusheqnL
  \end{flalign*}}

Here's an example of the output:

\documentclass[twoside]{scrartcl}
\usepackage{amsmath}% http://ctan.org/pkg/amsmath
\usepackage{lipsum}% http://ctan.org/pkg/lipsum
\usepackage{marginnote}% http://ctan.org/pkg/marginnote
\usepackage{everyshi}% http://ctan.org/pkg/everyshi
\def\flusheqnL{&} \def\flusheqnR{}%
\EveryShipout{%
  \ifodd\value{page}
    \gdef\flusheqnL{} \gdef\flusheqnR{&&}%
  \else
    \gdef\flusheqnL{&} \gdef\flusheqnR{}%
  \fi
}%

\begin{document}

\lipsum[1]
\marginnote{Is flush left (manually)
  \begin{flalign*}
    a&=1 &\\
    b&=1 &
  \end{flalign*}}
\lipsum[2]
\marginnote{How to make flush left automatically?
  \begin{flalign*}
    \flusheqnR a&=1 \flusheqnL \\
    \flusheqnR b&=1 \flusheqnL
  \end{flalign*}}
\lipsum[3-6]
\marginnote{Is flush right (manually):
  \begin{flalign*}
    && a&=1\\
    && b&=1
  \end{flalign*}}
\lipsum[7]
\marginnote{How to make flush right automatically?
  \begin{flalign*}
    \flusheqnR a&=1 \flusheqnL \\
    \flusheqnR b&=1 \flusheqnL
  \end{flalign*}}
\lipsum[8-9]
\end{document}

The redefinition of \flusheqnL and \flusheqnR has to be made global (via \gdef) in order for it to hold outside the group (within \EveryShipout).