Animation is generally often a bad idea as it will distract the audience from the presentation (see Beamer manual).
I've read that animation (ex: dissolve, moveto) should be possible between frame with at least Acrobat reader, but I didn't try them, and they are limited to the whole slide.
Smooth animation could be precalculated using the animate
package, as this nice example. I think that you could also move smoothly a part of a text between 2 points in a similar way.
Edit exemple of animation: production of AC current
\documentclass{beamer}
\usepackage{animate}
\usepackage{tikz}
\usetikzlibrary{decorations.markings}
\newcounter{angle}
\setcounter{angle}{0}
\begin{document}
\begin{frame}[fragile]{Production of AC current}{Alternator}
\begin{center}
\begin{animateinline}[loop,poster=first,controls]{10}
\whiledo{\theangle<720}{
\begin{tikzpicture}[scale=.7]
\path[use as bounding box] (-3.5,-4) -- (10,4);
%\draw (-3.5,-4) rectangle (10,4);
% 1/2 surface inf
\draw[black!50,thick] (2,-1)
arc[start angle=-90,end angle=90,x radius=.2cm, y radius=1cm];
\begin{scope}[rotate=\theangle]
% lignes de champ
\foreach \h/\X/\Y in {.85/1.6/.8, 1.1/2/1.1, 1.325/2.4/1.35,%
1.525/2.8/1.6} {
\draw [decoration={markings,
mark=between positions 0 and 1 step 1.5cm
with {\arrow{stealth}}},
postaction={decorate},color=brown!60] (0,\h)
circle[x radius=\X cm,y radius=\Y cm];
\draw [decoration={markings,
mark=between positions 0 and 1 step 1.5cm
with {\arrowreversed{stealth}}},
postaction={decorate},color=brown!60] (0,-\h)
circle[x radius=\X cm,y radius=\Y cm];
}
\end{scope}
% 1/2 surface sup
\draw[thick] (2,-1)
arc[start angle=-90,end angle=-270,x radius=.2cm,%
y radius=1cm];
% aimant
\begin{scope}[rotate=\theangle]
\fill[color=cyan!70] (-1,-.25) rectangle (0,.25);
\fill[color=red!70] (0,-.25) rectangle (1,.25);
\draw (-1,-.25) rectangle (1,.25);
\end{scope}
% calculation of the position
\pgfmathrad{\theangle}
\edef\myangle{\pgfmathresult}
\pgfmathparse{4 + .4 * \myangle}
\edef\myX{\pgfmathresult}
\pgfmathparse{2 * cos(\theangle)}
\edef\myY{\pgfmathresult}
\coordinate (O) at (4,0);
\begin{scope}
% axes
\draw[->] (O) -- ++(5.5,0) node[below]{$t$};
\draw[->] ([yshift=-2.5cm]O) -- ([yshift=2.5cm]O) node[left]{$I$};
\begin{scope}[xshift=4cm,xscale=0.4] % sinusoïde
% calcul clip
%\node at (1,1) { \myangle };
\clip (0,-2.5) rectangle (\myangle,2.5);
\draw[green,thick] (0,2) cos (1.5708,0) sin (3.1416,-2)
cos (4.7124,0) sin (6.2832,2) cos (7.8540,0)
sin (9.4248,-2) cos (10.9956,0) sin (12.5664,2);
\end{scope}
\draw[fill=green!30,draw=green] (\myX,\myY) circle[radius=.5mm];
\end{scope}
\end{tikzpicture}
%
%\addtocounter{angle}{720}
\addtocounter{angle}{5}
%\stepcounter{angle}
\ifthenelse{\theangle<720}{%
\newframe
}{%
\end{animateinline}
}
}
\end{center}
\end{frame}
\end{document}