This has good alignments, but the text part of item (Lol and Hackety hack.) shouldn't be too large:
\documentclass{article}
\begin{document}
First an equation.
\begin{equation}
f(x) = \sin(x)
\end{equation}
Then a list.
\begin{itemize}
\item Lol \hfill \makebox[0pt][r]{%
\begin{minipage}[b]{\textwidth}
\begin{equation}
y_t=h_t(\hat{x}_{t|t-1})
\end{equation}
\end{minipage}}
\item Hackety hack. \hfill \makebox[0pt][r]{%
\begin{minipage}[b]{\textwidth}
\begin{equation}
a = b
\end{equation}
\end{minipage}}
\end{itemize}
And another equation.
\begin{equation}
g(x) = \cos(x)
\end{equation}
\end{document}

$ $. You can not number an inline expression. – Sigur Dec 31 '12 at 11:07