I have something like the following:
Long paragraph with footnote.\footnote{footnote shtuff here}
Another long paragraph without a footnote.
\begin{wrapfigure}{r}{.5\textwidth}
% figure shtuff here
\end{wrapfigure}
The output is rather frightening:
How can I fix this? There are no figures previous this one and I don't mind raising it up on the page.
I know it's not really an answer to the question but I'd try to avoid wrapfigure altogether. There are two alternative packages called picinpar and picins. picins is often considered the successor of picinpar but I don't like it personally. In its documentation the amount of bad typography is only surpassed by the number of drop shadow effects.
picinpar will not solve all your problems and it doesn't support any floating as the R and L parameters to wrapfig do (as Stefan pointed out) but it will manage decent spacing, justification and possibilities to mitigate bad luck. You can (and must) pass the number of lines above the image as an argument. The syntax is a bit cryptic but the following example might illustrate its usage (sorry it's in German), as does the good package documentation.
If this doesn't help, try some related questions like How to wrap text around a figure? and wrapfigure cuts off images at the end of the page.
Ras parameter for positioning, that should allow Wrapfigure to float:\begin{wrapfigure}{R}{.5\textwidth}– Stefan Mar 12 '12 at 09:47