Why do one pixel wide lines look like a twisted ribbon on this DLP projector?
Since the pixel grid that the projector displays is a rectangular grid of rectangular pixels, how do you display something that isn't rectangular? Think about a pixel where the outline of the line falls half-way across it—half the pixel is in the line, and half out. How does that pixel display?

There are a couple of ways of doing it. You could set a threshold at which the pixel is either on or off and switch between the two. This would create a staircase on the horizontal line, where pixels were close to the point above and below the threshold. This wouldn't look that great unless the projector was extremely high resolution, where the jagginess was too small to see. The projector in the picture is nowhere near that level of resolution, so another technique to smooth out the jagginess is needed.



The technique is called Anti Aliasing. Where pixels are not fully illuminated or fully dark they have an in-between value of grey, proportional to the amount that the line covers them (this is a gross oversimplification, there is a whole science of signal processing behind how it happens in real anti-aliasing techniques). 

So a pixel that is half covered by the line might be 50% illuminated. This smooths out the appearance of the diagonal line, meaning that you get the appearance of a higher resolution and smoother image. 

However the anti-aliasing is not always exactly right. The variations in response curves for viewing devices (screens, projectors etc) means that sometimes the in-between levels that you see aren't what they are supposed to be in theory, meaning that some of the pixels are slightly too bright or dark, adding artefacts to the result. That's what you're seeing. 

To improve the image try adjusting or calibrating the projector or the device it is connected to, particularly the contrast or gamma.