The biblatex-mla package doesn't define a \fullcite command (it would have been very helpful to have mentioned that you were using this package in your question). Adapting some code (and naming convention) from the biblatex-apa package, based on Hanging references using \fullcite, here is a solution to your problem. Since MLA uses different author name ordering in footnote references and bibliography references but you want to be able to display both, we define a \fullcitebib command which will insert a properly formatted full bibliography entry in the text and a \fullcitefoot command which will insert a properly formatted footnote-style entry.
\documentclass{beamer}
\usepackage[style=mla,autocite=footnote]{biblatex}
\DeclareAutoCiteCommand{footnote}[f]{\footcite}{\footcites}
\setlength{\bibhang}{1.5em}
\makeatletter
\DeclareCiteCommand{\fullcitefoot}
{\renewcommand{\finalnamedelim}
{\ifnum\value{liststop}>2 \finalandcomma\fi\addspace\&\space}%
\list{}
{\setlength{\leftmargin}{\bibhang}%
\setlength{\itemindent}{-\leftmargin}%
\setlength{\itemsep}{\bibitemsep}%
\setlength{\parsep}{\bibparsep}}\item}
{\usedriver
{\DeclareNameAlias{sortname}{default}}
{\thefield{entrytype}}\finentry}
{\item}
{\endlist\global\undef\bbx@lasthash}
\DeclareCiteCommand{\fullcitebib}
{\renewcommand{\finalnamedelim}
{\ifnum\value{liststop}>2 \finalandcomma\fi\addspace\&\space}%
\list{}
{\setlength{\leftmargin}{\bibhang}%
\setlength{\itemindent}{-\leftmargin}%
\setlength{\itemsep}{\bibitemsep}%
\setlength{\parsep}{\bibparsep}}\item}
{\usedriver
{}
{\thefield{entrytype}}\finentry}
{\item}
{\endlist\global\undef\bbx@lasthash}
\makeatother
\usepackage{filecontents}
\begin{filecontents}{\jobname.bib}
@article{Bli74,
author = {Blinder, Alan S.},
year = {1974},
title = {The economics of brushing teeth},
journaltitle = {Journal of Political Economy},
volume = {82},
number = {4},
pages = {887--891},
}
\end{filecontents}
\addbibresource{\jobname.bib}
%\renewcommand{\footnotesize}{\scriptsize} uncomment this if you want footnotes smaller
\begin{document}
\begin{frame}
This is a full citation in footnote style: \fullcitefoot{Bli74}.
This is a full citation in bibliography style: \fullcitebib{Bli74}
\end{frame}
\begin{frame}
\printbibliography
\end{frame}
\end{document}

biblatex-mla. This was really important information that you should have mentioned in your question originally. (As a result, two people gave good answers that don't actually work for you.) – Alan Munn Dec 17 '11 at 16:13