Is there a typo in Sims(2002) paper on solving linear expectations model? Here's the Sims(2002) paper. It's equal to the published version.

The author gives the following example: 



And tries to write it in the matrix notation of (1) in the paper.

However, his solution - in (4) - puts $\epsilon (t)$ in the first equation of (2) instead of $\nu (t-1)$, and $\nu (t-1)$ instead of $\epsilon (t)$. Is this correct, and why?

Also, when I try to write the the first equation of (2) the time notation doesn't match. The other two equations in (2) do match.

Any help would be appreciated.
Yes the $z(t)$ column vector, as it appears in $(4)$ is written upside-down in the translation. Also the first equation in $(2)$ is translated lagged once, i.e. the translated system describes the $w(t-1)$ equation.

Finally there is a typo in the $\Gamma_1$ matrix, there is a void 6th column that should be ignored, and $\theta$ should be in the 4th column not in the 5th (because it multiplies $u(t-1)$.