This seems to be a bug in pgfplots, I will take care of it.
Although I do not see the mistake, I can say how to AVOID the problem until the bugfix is ready - provided you are running with pgfplots 1.6.1 (the most recent stable):
adding
\pgfplotsset{cell picture=if necessary}
to your preamble (or \begin{axis}[..., cell picture=if necessary] to selected axes) will fix it.
ATTENTION: in this case, you need to move remember picture from \begin{axis} to \begin{tikzpicture}!
You can also say cell picture=false. In this case you will receive error messages if pgfplots really needs the initial setting (which is cell picture=true as you might have guessed).
Technical explanation:
I see that it is somehow related to the fact that pgfplots creates a so-called "cell-picture" and moves it to implement its positioning choices (the anchors). A cell-picture means that it creates an additional \tikzpicture...\endtikzpicture internally just like a pgf matrix.
The initial value cell picture=true is mainly for backwards compatibility. In general, it has advantages to avoid cell pictures. They are necessary if you choose an anchor which is NOT in the list
north, north west, west, south west, south, south east, east, north
east, north, center, origin, above origin, left of origin, right of origin, below origin.
For example, the choice anchor=above north requires a cell picture.
EDIT at July 2016
@ Elmar pointed out that the issue is not resolved completely and he provided the minimal example
%compile with: pdflatex -shell-escape main && make -f main.makefile && pdflatex main
\documentclass{article}
\usepackage{pgfplots}
\usetikzlibrary{external}
\tikzset{external/export=false, external/mode=list and make}
\tikzexternalize
\pgfplotsset{compat=1.13}
\begin{document}
\tikz[remember picture] \node {X};
\tikzset{external/export=true}
\begin{tikzpicture}
\begin{axis}[clip=false]
\addplot {x};
\node (A) at (yticklabel cs:0.5) {A};
\end{axis};
\node at (A) {B};
\end{tikzpicture}
\end{document}
and he has a point - there are still issues. In his example, the problem is caused by an entry in the main.aux file which refers to the "remembered position" -- it is accidentally associated with the second image.
I will look into it. For now, a workaround appears to be to not optimize the first picture away as this will result in correct internal picture identifiers when externalizing the graphics:
%compile with: pdflatex -shell-escape main && make -f main.makefile && pdflatex main
\documentclass{article}
\usepackage{pgfplots}
\usetikzlibrary{external}
\tikzset{external/export=false, external/mode=list and make}
\tikzexternalize
\pgfplotsset{compat=1.13}
\begin{document}
{\tikzset{external/optimize=false}%
\tikz[remember picture] \node {X};
}%
\tikzset{external/export=true}
\begin{tikzpicture}
\begin{axis}[clip=false]
\addplot {x};
\node (A) at (yticklabel cs:0.5) {A};
\end{axis};
\node at (A) {B};
\end{tikzpicture}
\end{document}
remember pictureoption to the tikzpicture env. but I can reproduce this. This can be also be seen within the same TikZ picture withoutoverlayorremember picture. Using\draw (c) -- (0,0);results with the same output. – percusse Sep 16 '12 at 16:53