Notes on textpos and pgfpages
When pgfpages is active, note that any textblocks positioned through use of the textpos package with the absolute option will most likely be incorrectly positioned, as witnessed here. I haven't entirely worked out what the positioning behaviour is though...
Also, you should be aware of other warnings that textpos emits in your MWE, even though they don't appear to influence the output in this case (these warnings can be avoided by ensuring there is a paragraph break immediately before the textblock environments):
Package textpos Warning: environment textblock* not in vertical mode.
(textpos) Environment textblock* should not have any text
(textpos) or printable material appearing before it.
(textpos) Alignment may work out wrongly.
I therefore present a solution that doesn't rely on using textpos, and therefore has other advantages. Alternative options include use of textpos but only using relative positioning; in this case, one should ensure that all textblocks have their origins at fixed locations in the slide (else they may move as the slide content changes), and this is harder.
Solution avoiding textpos
My idea is to use the footnote facilities instead (one can still keep the original formatting and it should interact well with multiple \sources and real footnotes). I have shrunk the height of the beamercolorbox used by \source and the distance between the footnotes:
\documentclass{beamer}
\usepackage{pgfpages}
\setbeameroption{show notes on second screen}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\setbeamercolor{framesource}{fg=gray}
\setbeamerfont{framesource}{size=\tiny}
\makeatletter
\renewcommand{\footnoterule}{}
\define@key{beamerfootnote}{nonumber}[true]{\edef\beamer@footarg{0}\def\@makefnmark{}}% have to set a number in \beamer@footarg, then it won't be automatically generated one. setting \@makefnmark to be empty means the number isn't printed. but only use this in a group else it affects following footnotes!
% instead of 'nonumber', could just use 0 as an optional argument to \footnote, but OP reports that keyval complains about this in some situations
% http://tex.stackexchange.com/questions/89539
\newcommand{\source}[1]{{\footnote[nonumber]{%
\begin{beamercolorbox}[right,wd=\dimexpr\hsize-1.8em\relax]{framesource}
\usebeamerfont{framesource}\usebeamercolor[fg]{framesource} Source: {#1}
\end{beamercolorbox}}}}
\setlength{\footnotesep}{0cm}%\footnotesep is the space between footnotes (generated with a \rule)
\makeatother
% inspired by [beamer: footnote text collides with navigation symbols](http://tex.stackexchange.com/a/5855)
\addtobeamertemplate{sidebar right}{\setbeamertemplate{navigation symbols}{}}{}
\addtobeamertemplate{footline}{\hfill\usebeamertemplate***{navigation symbols}%
\hspace*{0.1cm}\par\vskip 2pt}{}
\title{MWE}
\begin{document}
\begin{frame}{title}
a diagram
\footnote{a real footnote}%
\footnote{a real footnote}%
\source{some article or url}%
\source{some article or url}%
\footnote{a real footnote}%
\end{frame}
\end{document}

Note that the magic number 1.8em that needs to be removed from the width of the beamercolorbox (to avoid overfull \hboxes) is defined in the default beamer template for footnote, and this is the space reserved for the footnote number:
\defbeamertemplate*{footnote}{default}
{
\parindent 1em\noindent%
\raggedright
\hbox to 1.8em{\hfil\insertfootnotemark}\insertfootnotetext\par%
}
Other notes about pgfpages
Note that other considerations also apply when using pgfpages (even if indirectly), such as page numbers etc. The main advice is to fully compile the document without pgfpages active, then activate it and compile again with \nofiles invoked also.
absoluteoption to thetextpospackage in combination with the use ofpgfpages(which is internally used bybeamerwhen you enable the optionshow notes on second screen), and this type of problem has come up repeatedly. – cyberSingularity Jan 06 '13 at 00:24