Hi,
I tried to do a wood texture with the calygraphytool and it worked, however when I try to export it to png it fails.

here's my (no comments;)) image

As you can see, there's a huge, untextured rectangle in my door. Is there a way to get rid of this?

I can't see the gaps, due to their size I think. Could you upload the SVG file?

Unfortunatly inkscape crashed and the door is lost. However, I can give you the current svg as the problem occurs to the wooden bars as well.
Here's a bigger version with door:
http://imagesload.net/img/haus4x.png
here's the svg without door:
http://npshare.de/files/f6f2e16a/haus.svg

There are known glitches with Inkscape's renderer when exporting to bitmap - omitting or only partially rendering some paths (depending on path geometry and export resolution), e.g.

• Bug #189214 in Inkscape: “curve is exported badly (but displayed correctly)”

This issues will likely (or hopefully ;) ) stop once Inkscape switches the internal renderer to cairo, planned for 0.49).