Without the \pause command, "On the first or third slide" has no specification for when to appear, which means it always appears. With the \pause command, it uncovers the list items one at a time until they are all uncovered, and then pauses again, which is why you have the repeat slide (since nothing changes between uncovering the last item and pausing).
The solution is to specify when you want the items after the list to appear. One method of accomplishing this is to surround it with an \uncover command:
\documentclass{beamer}
\begin{document}
\begin{frame}
\begin{itemize}[<+->]
\item On the first slide
\end{itemize}
\uncover<+->{
On the second slide
}
\end{frame}
\end{document}
Edit
In response to your edit, here's another way to solve your problem. You are using \pause in combination with the list option [<+->], which adds its own pauses and so results in double pauses sometimes. If you really prefer to not give up \pause, then you can fix your example's behaviour by using it exclusively:
\documentclass{beamer}
\begin{document}
\begin{frame}
On the first slide
\pause
\begin{itemize}
\item On the second slide.
\pause On the third slide
\pause\item On the fourth slide
\end{itemize}
\end{frame}
\end{document}
This also works in your first example:
\documentclass{beamer}
\begin{document}
\begin{frame}
\begin{itemize}
\item On the first slide
\pause\item On the second slide
\end{itemize}
\pause On the third slide
\end{frame}
\end{document}
The potential down side of this approach is that \pause stops everything after it on the current frame from appearing until the pause has passed, even if you specify that it should appear earlier. For example,
\documentclass{beamer}
\begin{document}
\begin{frame}
Here are important points:
\begin{itemize}
\item Point on Slide 1
\pause\item Point on Slide 2
\pause\item Point on Slide 3
\end{itemize}
\uncover<1-3>{
I want to emphasize this on every slide:\\ Always remember these points!\\ (But it only appears on the third slide)
}
\end{frame}
\end{document}
On the other hand, with less code you can achieve this effect simply:
\documentclass{beamer}
\begin{document}
\begin{frame}
Here are important points:
\begin{itemize}[<+->]
\item Point on Slide 1
\item Point on Slide 2
\item Point on Slide 3
\end{itemize}
Always remember these points!
\end{frame}
\end{document}
I am not sure of what exactly you need, but here are few options:
With \visible
\documentclass{beamer}
\usepackage{beamerthemesplit}
\usepackage{stmaryrd}
\usepackage{comment}
\begin{document}
\frame{\titlepage}
\frame{
\frametitle{some title}
\begin{enumerate}
\item 1st text to be revealed
\visible<3->{\begin{itemize}
\item 3rd text to be revealed
\end{itemize}}
\visible<2->{
\item 2nd text to be revealed
}
\visible<4->{
\begin{itemize}
\item 4th text to be revealed
\end{itemize}
}
\end{enumerate}
}
\end{document}
Or even simpler
\documentclass{beamer}
\usepackage{beamerthemesplit}
\usepackage{stmaryrd}
\usepackage{comment}
\begin{document}
\frame{\titlepage}
\frame{
\frametitle{some title}
\begin{enumerate}
\item<1-> 1st text to be revealed
\begin{itemize}
\item<3-> 3rd text to be revealed
\end{itemize}
\item<2-> 2nd text to be revealed
\begin{itemize}
\item<4-> 4th text to be revealed
\end{itemize}
\end{enumerate}
}
\end{document}
Best Answer
Have a look at section 9.6.4 and section 23.1 of the
beamermanual: You can use a dot in the overlay specification (e.g.<.->). The dot is replaced by the current value ofbeamerpausesminus one, so if you use\item<.->, this item is shown simultaneously with the previous\item.For example, if you have a list with four items and you want to show the second and the third one at the same time, use
\item<.->for the third item to override the default overlay specification: