vector arrow with superscript

I don't really know why the result is bad; I suspect it has to do with the width of the letter. I wouldn't use such a notation, but that's a personal opinion.

With

\vec{o}^{\,t}

the superscript is moved a bit to the right. One might perhaps let TeX do some computations in order that the shift to the right of the superscript is automatic.

Try this:

\documentclass{article}
\usepackage{esvect}
\begin{document}
$\vv{o}^t \ \vv{o^t}$
$\vec{o}^{\,t}$
\end{document}

(I have included egreg's code to make the comparison easier.)

The first two are done using the esvect package, the third is egreg's code.

How about something like

\documentclass{article}

\makeatletter
\newcommand{\vo}{\vec{o}\@ifnextchar{^}{\,}{}}
\makeatother

\begin{document}

$\vec{o}^t o$ $\vo^t o$ 

$\vec{o} o$ $\vo o$

$\vec{o}^t_t o$ $\vo^t_t o$

\end{document}

This looks all right for $\vo^t$. (The ^ must be immediately after \vo.) I don't know how to make just the superscript shift in $\vo^t_t$.

Here is a discussion of how \@ifnextchar works.