Here's something that works with the example you posted, but might not work with more sophisticated overlay specifications. There are two parts to the method. The first is a little addition to the overlay code which tries to establish whether the current frame was explicitly mentioned, for example the 3 in \uncover<3->, or not, for example frame 4 in \uncover<4->. If explicitly mentioned, it sets a flag. The second part to the method is a little addition to pgfpages, imaginatively called pgfmorepages (CTAN and github), which - amongst other things - introduces the possibility of skipping a page when shipping out pages. So this looks for the flag set by the first part of the code and if it doesn't find it, it ignores the particular page.
There is a snag. You can't use the transparent option. That is because this does some look-ahead stuff and asks "Is this going to appear in a frame or two's time?" So it runs the overlay specifications with other frame numbers than the current one and that messes up the testing.
The other annoying bit is that each frame has to start with the command \mentionedsetup. This could be automated by adding it to one of the templates.
Here's the code with some sample frames.
%\url{http://tex.stackexchange.com/q/56990/86}
% 1. NO NOTES
\documentclass[]{beamer}
%% 2. DUAL-DISPLAY NOTES:
%\documentclass[hyperref={bookmarks=true}]{beamer}
\usepackage{pgfmorepages}
%\setbeameroption{show notes on second screen=left}
\makeatletter
\newif\if@mentioned
\@mentionedtrue
\pgfpagesdeclarelayout{1 on 1 with possible skip}
{
\def\pgfpageoptionborder{0pt}
}
{
\pgfpagesphysicalpageoptions
{%
logical pages=1,%
physical pages=1,%
first logical shipout=1,%
last logical shipout=1,%
current logical shipout=1,%
}
\pgfpagesphysicalpage{1}{
skip code={%
\if@mentioned
\pgfpagesshiptrue
\else
\pgfpagesshipfalse
\fi
}
}
\pgfpageslogicalpageoptions{1}
{%
center=\pgfpoint{.5\pgfphysicalwidth}{.5\pgfphysicalheight},%
}%
}
\pgfpagesuselayout{1 on 1 with possible skip}
\def\slidereferenced{%
\ifbeamer@inframe
\global\@mentionedtrue
\fi
}
\def\mentionedsetup{%
\ifnum\beamer@slideinframe=1
\global\@mentionedtrue
\else
\global\@mentionedfalse
\fi
}
\expandafter\let\csname
beamerx@\string\beamer@inframenote\endcsname\relax
\renewcommand<>{\beamer@inframenote}[2][]{}
\def\beamer@decodeuntil-#1,{%
\ifnum1<\beamer@minimum\global\beamer@minimum=1\fi%
\ifnum#1>\beamer@slideinframe\global\beamer@anotherslidetrue\beamer@localanotherslidetrue\fi%
\ifnum\beamer@slideinframe>#1\else\gdef\beamer@doifnotinframe{\beamer@doifinframe}\fi%
\ifnum\beamer@slideinframe=#1\relax\slidereferenced\fi%
\beamer@@decode}
\def\beamer@decodeto#1,{%
\ifnum#1<\beamer@minimum\global\beamer@minimum=#1\fi%
\ifnum#1>\beamer@slideinframe\global\beamer@anotherslidetrue\beamer@localanotherslidetrue\fi%
\ifnum#1>\beamer@slideinframe\else\gdef\beamer@doifnotinframe{\beamer@doifinframe}\fi%
\ifnum\beamer@slideinframe=#1\relax\slidereferenced\fi%
\beamer@@decode}
\def\beamer@decodebetween#1#2,{%
\ifnum#1<\beamer@minimum\global\beamer@minimum=#1\fi%
\ifnum#1>\beamer@slideinframe\global\beamer@anotherslidetrue\beamer@localanotherslidetrue\fi%
\ifnum#2>\beamer@slideinframe\global\beamer@anotherslidetrue\beamer@localanotherslidetrue\fi%
\ifnum#1>\beamer@slideinframe\else\ifnum#2<\beamer@slideinframe\else\gdef\beamer@doifnotinframe{\beamer@doifinframe}\fi\fi%
\ifnum\beamer@slideinframe=#1\relax\slidereferenced\fi%
\ifnum\beamer@slideinframe=#2\relax\slidereferenced\fi%
\beamer@@decode}
\def\beamer@decodeone#1,{%
\ifnum#1<\beamer@minimum\global\beamer@minimum=#1\fi%
\ifnum#1>\beamer@slideinframe\global\beamer@anotherslidetrue\beamer@localanotherslidetrue\fi%
\ifnum#1=\beamer@slideinframe\gdef\beamer@doifnotinframe{\beamer@doifinframe}\fi%
\ifnum\beamer@slideinframe=#1\relax\slidereferenced\fi%
\beamer@@decode}
\makeatother
\usepackage[english]{babel}
\mode<presentation>{
\usetheme{Warsaw}
% \setbeamercovered{transparent}
}
\begin{document}
\begin{frame}{Testing}
\mentionedsetup
\uncover<1->{hello}
\uncover<3->{world}
\uncover<5->{greetings}
\uncover<7->{earthlings}
\end{frame}
\begin{frame}{Introduction}{}
\mentionedsetup
\begin{itemize}
\item hello world
\uncover<1->{\item Here is my first point}
\uncover<2->{\item Here is my second point}
\uncover<4->{\item With notes on, I would expect it to take two
clicks to get here from the last point, since there are two notes. But
with them off, I would expect it to take one click.}
\uncover<5->{\item This is my third point. I have four notes about
this point, so with notes on, it should take three more clicks to get
to the next slide. With them off, however, it should take one. }
\end{itemize}
\note[item]<1->{Here is a note about my first point}
\note[item]<2->{Here is a note about my second point}
\note[item]<3->{Here is \textbf{another} note about my second point}
\note[item]<4->{Here is a note about my third point}
\note[item]<5->{Here is the second of several more notes about my
third point}
\note[item]<6->{Another one}
\note[item]<7->{And another}
\end{frame}
\begin{frame}{Another slide}{}
\begin{itemize}
\uncover<1->{\item Not much to say here}
\end{itemize}
\end{frame}
\end{document}
Oh, and we have to redefine the \note command. Even when the notes aren't shown, the command is processed. So we have to redefine it to be a NO-OP to ensure that the resulting overlays aren't read.
Here's the first few frames of the above, showing that frames 2,4,6 get skipped.
You do need to tell beamer what you want to appear in each frame of the handout version. You can use \onslide specifications to do this so that you do not need to modify the existing overlay specifications at all. (I'm not sure this is what you want - probably not.)
The following code modifies your MWE so that, in presentation mode, there would actually be 10 slides within the frame. These are then placed on slides 1 or 2 of the handout. This is a waste of code: if you only want to show slide 5 and slide 10, you do not need two \againframe but only one. But, anyway, with the two:
\documentclass[handout]{beamer}
\begin{document}
\begin{frame}<1-| handout:0>[label=foo]{My only frame}
\begin{enumerate}[<+->]% or whatever you like for presentation mode
\onslide<1-| handout:1-2>
\item Item \arabic{enumi}
\item Item \arabic{enumi}
\item Item \arabic{enumi}
\item Item \arabic{enumi}
\item Item \arabic{enumi}
\onslide<1-| handout:2>
\item Item \arabic{enumi}
\item Item \arabic{enumi}
\item Item \arabic{enumi}
\item Item \arabic{enumi}
\item Item \arabic{enumi}
\end{enumerate}
\end{frame}
\againframe<0| handout:1>{foo}
\againframe<0| handout:2>{foo}
\end{document}
More efficiently with only one repeat:
\documentclass[handout]{beamer}
\begin{document}
\begin{frame}<1-| handout:1>[label=foo]{My only frame}
\begin{enumerate}[<+->]% or whatever you like for presentation mode
\onslide<1-| handout:1-2>
\item Item \arabic{enumi}
\item Item \arabic{enumi}
\item Item \arabic{enumi}
\item Item \arabic{enumi}
\item Item \arabic{enumi}
\onslide<1-| handout:2>
\item Item \arabic{enumi}
\item Item \arabic{enumi}
\item Item \arabic{enumi}
\item Item \arabic{enumi}
\item Item \arabic{enumi}
\end{enumerate}
\end{frame}
\againframe<0| handout:2>{foo}
\end{document}
I'm not sure how this could apply to article mode since then there are no frames or slides.
Best Answer
I've isolated the problem down to the
infolinesouter theme and specifically the line:towards the end. What seems to be happening is that the note templates aren't quite configured correctly with regard to changing the margins. Some length that the
itemizeenvironment uses to figure out its width is not getting set correctly when using notes. As I've not much idea which lengths these are, and which beamer mucks about with, I've not much of an idea as to how to properly fix this.However, I have a way to improperly fix this. What I found was that by putting the note within a
minipageenvironment of the right width worked. That reset all the correct widths to the right ones without my having to know any of the 'orrible details! Of course, that's a bit annoying to put in every time so it's possible to force it by modifying the beamer template for the notes page. Copying out the default one, and adding the necessary lines, I arrived at:and that seemed to work fine!