Inkscape 0.91 and above has the ability to toggle antialiasing. This can be accessed through the Document Properties window (Shift+Ctrl+D). When turned on, which is the default, this image of an array of triangles looks like this.
When turned off the image looks smoother.
As others have mentioned, this currently has no effect on the png export. Antialiasing is still turned on and the gaps between the triangles still visible.
What Inkscape is doing when you disable antialiasing is adding
shape-rendering="crispEdges" to the file. Open your SVG in a text editor and look somewhere around line 19 and you should see it.
Luckily, this tag is read and adhered to when importing the SVG into GIMP. GIMP can import an SVG and set the import resolution, meaning that you can scale your png on import to be your desired size. It will crop it to the page boundaries.
You can now save the image and antialiasing will be disabled.
This has been reported as a bug a couple of times: