Why in the second case the spacing is correct and not in the first ?
Maybe not fully correct in the second between + and u ?
\documentclass[xcolor=dvipsnames]{beamer}
\begin{document}
\begin{frame}
\begin{equation*}
5 \only<1>{\textcolor{red}{+}}6+7
\end{equation*}
\begin{equation*}
\frac{\partial u}{\partial t}= \only<1>{\textcolor{red}{+u(n,t)}u(n+1,t)}\only<2>{u(n,t)\textcolor{red}{u(n+1,t)}} -u(n,t)u(n-1,t)
\end{equation*}
\end{frame}
\end{document}

5+6+7with 5{+}6+7. Curly braces around+` (and other math operators) eat space around it. The same happens when you change their color an way as you do. – Zarko Aug 15 '15 at 07:33{\color{red}\,+\,}. For better way ... temporary I haven't clue. – Zarko Aug 15 '15 at 07:50\begingroup\color{red}+\endgroup. – Heiko Oberdiek Aug 15 '15 at 07:50