Sorry for not getting back! I didn’t subscribe to this thread.
Well, the resolution of your rendered image depends basically on the dimensions that you rendered it out in. If you rendered it out in 960x480, the resolution isn’t going to be that good. However, if you rendered it with a dimension of 1920x960 (which is twice as big as 960x480), the resolution will be noticeably better.
The resolution of the rendered view I believe depends on the resolution of your monitor. if your monitor has good quality graphics capabilities, it should display up to the resolution of your monitor.
For some reason (maybe because I’ve done something wrong) textured view is’t working for me in the Blender Render, so I have no idea why it is that it looks better in textured view. I know that blender blurs the texture’s pixels when rendering, or at least it does in BI. I don’t know if it blurs the texture’s pixels in textured view, but if it didn’t, the image textures might be a little sharper.
Also, when you render something, and an object’s edge isn’t exactly filling in a pixel (like filling in only part of it), then blender will average the amount of the object that’s filling in the pixel vs. whatever else is (another object, the sky, etc.). This usually leads to softer edges. In the textured view, I’d guess that it doesn’t average all that stuff to so that it can speed up the viewport.
I’m sorry if this is terribly complicated. I’m not really good at explaining things.
P.S. Here is the URL for pasteall: http://www.pasteall.org/