Is there a penalty to using two <nav> elements in a <header>
Short answer: no there is not (probably)
Longer answer: the HTML5 spec itself is a bit fluffy on the subject: http://dev.w3.org/html5/spec/Overview.html#the-nav-element
The thing is that they designate the <nav>
element to 'major' navigation blocks, but leave it to the imagination (of both developers and parsers) what that means. As you can see they even provided an example where they exclude the "site-wide" from the navigation block.
<body itemscope itemtype="http://schema.org/Blog">
<header>
<h1>Wake up sheeple!</h1>
<p><a href="news.html">News</a> -
<a href="blog.html">Blog</a> -
<a href="forums.html">Forums</a></p>
<p>Last Modified: <span itemprop="dateModified">2009-04-01</span></p>
<nav>
<h1>Navigation</h1>
<ul>
<li><a href="articles.html">Index of all articles</a></li>
<li><a href="today.html">Things sheeple need to wake up for today</a></li>
<li><a href="successes.html">Sheeple we have managed to wake</a></li>
</ul>
</nav>
</header>
They seem to do that because they consider limiting the number of links in nav elements a plus for readability (think screen readers etc).
It is probably a bit too early to know what the search engines are going to do, but it seems safe to think that they will attach more importance to nav element links to detect the structure of you site and maybe more so if you have less of them...
My impression: Twitter and Facebook links seem certainly out, support and blog are debatable