I am really thankful for the new feature to add a widget to the header of the theme.
Please find some suggestions for improvements below.

A <tr> element is missing in functions.php on row 323. It would be good to add one.
echo '<table id="' . $area_id . '" class="bfa_widget_area" style="table-layout:fixed; width: 100%" cellpadding="0" cellspacing="0" border="0"><tr>';

It is not really very easy to get the widget inside the %logo% area. Would it be possible to split the %logo% into smaller parts like %title&, %rss%, %search% so the widget can be placed in between? This way the header can be kept compact. Currently following modifications were needed to get the desired layout:

Add a div around the table for the header in functions.php:
echo '<div id="bfa_widget_div"><table id="' . $area_id . '" class="bfa_widget_area"

A <div> is needed because following style sheet entries do to work correctly for a table:
div#header_widget_div{position:absolute;white-space:nowrap;overflow:hidden;left:500px;right:200p x;top:24px;z-index:1;}

And for IE it is needed to add the correct height:98px; too.

Results can be seen on our family weblog: hein.nu.
Note the effect when you make the browser window smaller (or when viewed under higher/lower resolution).

The missing tr was added in 3.4.2, along with few other improvements. Splitting up the header further is on the todo list