I was asked to try and put the scale labels for the yticks not right above the north west corner of the plot as it is rather unusual. Personally, I tend to agree. It works easily but above left might be a bit better. But actually, putting it right above the label for the y-axis, then rotated 90 degrees, is preferable.
Based on Jake's post here, I got the idea to position the scale right above the ylabel by anchoring it to the ylabel node for each groupplot. But this does not work for a groupplot for reasons I have not yet figured out.
But all in all, I intended to use a reliable method to anchor the scale labels to xlabel and ylabel because fine-tuning the positions is an immensely time-consuming task. :(
Is this possible, to anchor the tick scale labels at the north end of the ylabel in a groupplot?
Really cool mockup of what I would like to have (the blue, funny looking scale labels are the ones I want, please imagine the red one right next to the xlabel as well)

MWE (does not work)
\documentclass[
a4paper
]{scrartcl}
\usepackage{
lmodern,
tikz,
pgfplots,
}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepgfplotslibrary{groupplots}
%\pgfplotsset{
%x label style={at={(rel axis cs:0.5,-0.15)}, name=xlabel},
%y label style={at={(rel axis cs:-0.2,0.5)}, name=ylabel},
%}
\begin{document}
\begin{center}
\begin{tikzpicture}[font=\small]
\begin{groupplot}[
group style={
group size=2 by 1,
horizontal sep=0.2cm,
vertical sep=1.5cm,
ylabels at=edge left,
yticklabels at=edge left,
},
%
ymin=300,
ymax=1300,
%
xlabel={The label for the x-axis},
ylabel={Some y-values},
%
xlabel style={at={(rel axis cs:0.5,-0.15)}, name={xlabel} },
ylabel style={at={(rel axis cs:-0.2,0.5)}, name={ylabel}},
legend style={at={(xlabel.south)}, anchor=north, yshift=-1ex},
%
every x tick scale label/.append style={
at={(xlabel.east)}, anchor=west, inner sep=0pt
},
every y tick scale label/.append style={
at={(ylabel.north)}, rotate=90, anchor=south, inner sep=0pt
},
%
scale ticks above exponent={2},
]
\nextgroupplot
\addplot[only marks] coordinates{(2000,1200) (3000,500)};
\addlegendentry{Word}
\nextgroupplot
\addplot[only marks] coordinates{(2000,1200) (4000,400)};
\addlegendentry{Text}
\end{groupplot}
\end{tikzpicture}
\end{center}
\end{document}

\pgfplotsset{ henry's scale label/.style={ y coord trafo/.code=\pgfmathparse{##1/(1e#1)}, ylabel/.append={$\ \cdot{10^{#1}}$} } }you can callhenry's scale label=3in youraxisoptions to get the desired output. – Jake Sep 18 '14 at 19:57at={(0,1)}, above left, yshift=SOMEVALUE. "Less code is better", kind of... sort of. :) Thank you for looking into it, I appreciate it. – henry Sep 18 '14 at 20:26xshiftcommand exactly the length of whatever lengthhenry's scale labelmight add to the originalxlabel? – henry Sep 23 '14 at 20:41xlabel, you can simply attach the scale label to the side of thexlabel. I've added an answer. – Jake Sep 24 '14 at 05:07