Footnotes and footnote citations are problematic inside captions; as a workaround, you can use \footnotemark inside the \caption and \footcitetext{<text>} outside the caption:
\documentclass{beamer}
\begin{filecontents*}{mybibfile.bib}
@ARTICLE{authora,
author = {A. Aaaaa},
title = {Some article},
journal = {Journal of Dummy Article Names},
year = {2012},
volume = {99},
pages = {1-5}
}
@ARTICLE{authorb,
author = {B. Baaaa},
title = {Another article},
journal = {Journal of Dummy Article Names},
year = {2012},
volume = {99},
pages = {6-10}
}
@ARTICLE{authorbb,
author = {B. Baaaa},
title = {Another dup article},
journal = {Journal of Dummy Article Names},
year = {2012},
volume = {99},
pages = {6-10}
}
\end{filecontents*}
\usepackage[style=verbose-note,autocite=footnote,abbreviate=true,backend=bibtex]{biblatex}
\addbibresource{mybibfile.bib}
\usetheme{CambridgeUS}
\title{Beamer}
\author{Anyone}
\begin{document}
\begin{frame}
\frametitle{Introduction}
\begin{itemize}
\item ItemA~\footcite{authora} %This works
\item ItemB
\end{itemize}
\end{frame}
\begin{frame}
\frametitle{Introduction}
\scriptsize
\begin{table}
\centering
\begin{tabular}{|l|l|}
\hline 1 & 2 \\
\hline a & b \\
\hline
\end{tabular}
\caption{This only appears once~\footnotemark.}
\end{table}
\footcitetext{authorb}
\end{frame}
\begin{frame}
\frametitle{Introduction}
\scriptsize
\begin{table}
\centering
\begin{tabular}{|l|l|}
\hline 1 & 2 \\
\hline a & b \\
\hline
\end{tabular}
\caption{This appears once~\footnotemark.}
\end{table}
\footcitetext{authorbb}
\end{frame}
\end{document}
As a side note, in beamer there's no need to use placement specifiers for floats since beamer internally deactivates the floating mechanism.
You just need to define different templates for article and presentation modes. If you include
\setbeamertemplate{frametitle}{\marginnote{\insertframetitle}}
in printable.tex preamble then frame title will appear on the margin if you are also processing frames in article version. (\marginnote is defined in marginnote package)
In your example, all frame contents is skipped because it is preceded by \mode<presentation>. Instead you can use something like:
\begin{frame}
\frametitle{Foo Bar}
\only<beamer>{%
\begin{itemize}
\item Foo
\item Bar
\item Baz
\end{itemize}%
} %<- \only<beamer> closing
\end{frame}
This way, only frame contents will be skipped while frametitle is processed and printed as a margin note. You don't need to include any \marginpar{Foo Bar} into next paragraph.
Please, look at Changing \mode in beamer makes a new paragraph. Is it possible to avoid it? and How to better adjust placement of frametitle converted to marginpar in beamerarticle? and you will see why I prefer to use \only and \marginnote.
Your complete example adapted with previous solution is
% === printable.tex =======================================
\documentclass{scrartcl}
\usepackage{beamerarticle}
\usepackage{marginnote}
\setbeamertemplate{frametitle}{\marginnote{\insertframetitle}}
\begin{document}
\input{contents}
\end{document}
% === end of printable.tex ================================
%
% === slides.tex ==========================================
\documentclass{beamer}
\begin{document}
\input{contents}
\end{document}
% === end of slides.tex ===================================
%
% === contents.tex =======================================
\mode*
Lorem ipsum dolor sit amet, consectetur adipiscing elit.
Fusce laoreet dui vestibulum tortor luctus porttitor.
Aliquam dictum ipsum condimentum, auctor augue in,
consectetur lacus. Morbi auctor posuere scelerisque.
Aenean vel enim sit met orci rutrum fermentum faucibus et
mauris. Pellentesque tempor felis in imperdiet accumsan.
Mauris auctor pretium nulla et tincidunt.
\begin{frame}
\frametitle{Foo Bar}
\only<beamer>{\begin{itemize}
\item Foo
\item Bar
\item Baz
\end{itemize}}
\end{frame}
\mode*
Mauris malesuada nisl sit amet nisl
eleifend tincidunt. Sed sed libero scelerisque, ultrices
elit a, lacinia mi. Mauris nec semper metus, eget
pellentesque leo. Donec volutpat aliquam aliquam. Nunc
vel neque scelerisque, aliquam augue eget, gravida felis.
Suspendisse vel molestie libero.
% === end of contents.tex =================================
Note: A very nice example to understand how to work with beamerarticle to produce presentations and printed version from same sources is a-lecture. It's written by Till Tantau and is part of beamer distribution, so probably it's in your computer. Take a look at it!
Addition by vwegert:
With the help of the package environ, I managed to define an environment that -- in contrast to the open \only<beamer>{ command -- does not wreak havoc with the syntax highlighting, pretty printer and other tools:
% === printable.tex =======================================
\documentclass{scrartcl}
\usepackage{beamerarticle}
\input{preamble}
\setbeamertemplate{frametitle}{\marginpar{\insertframetitle}}
\begin{document}
\input{contents}
\end{document}
% === end of printable.tex ================================
% === slides.tex ==========================================
\documentclass{beamer}
\input{preamble}
\begin{document}
\input{contents}
\end{document}
% === end of slides.tex ===================================
% === preamble.tex =======================================
\usepackage{environ}
\NewEnviron{onlybeamer}{\only<beamer>{\BODY}}
% === end of preamble.tex =================================
% === contents.tex =======================================
\mode*
Lorem ipsum dolor sit amet, consectetur adipiscing elit.
Fusce laoreet dui vestibulum tortor luctus porttitor.
Aliquam dictum ipsum condimentum, auctor augue in,
consectetur lacus. Morbi auctor posuere scelerisque.
Aenean vel enim sit met orci rutrum fermentum faucibus et
mauris. Pellentesque tempor felis in imperdiet accumsan.
Mauris auctor pretium nulla et tincidunt.
\begin{frame}
\frametitle{Foo Bar}
\begin{onlybeamer}
\begin{itemize}
\item Foo
\item Bar
\item Baz
\end{itemize}
\end{onlybeamer}
\end{frame}
\mode*
Mauris malesuada nisl sit amet nisl
eleifend tincidunt. Sed sed libero scelerisque, ultrices
elit a, lacinia mi. Mauris nec semper metus, eget
pellentesque leo. Donec volutpat aliquam aliquam. Nunc
vel neque scelerisque, aliquam augue eget, gravida felis.
Suspendisse vel molestie libero.
\mode<all>
% === end of contents.tex =================================
Best Answer
You can label each frame
\begin{frame}[label=both]and then useA sample: