In 0.48 setting the background color actually work for most of the transparent/semitransparent pixels, which takes care of problem #1. However problem #2 still happens. To fix this I have to use an image program like Photoshop or GIMP, however it is an annoying process, and way to time consuming when I have to fix this everytime I export a PNG.
Now if Inkscape had a specific function to force one color upon ALL transparent and semitransparent pixels, that'd be pretty neat. Is there such a function or extension around?
The images below show screenshots from a game I am making where interpolation of colors between pixels is applied. Interpolation uses the color of transparent pixels to smooth the display of images to avoid ugly pixelation. That is where a wrong (for example black or white) color on transparent pixel creates a problem, as seen on the screenshots.

