Headers do seem the best place for a non vendor specific standard to be set. I'd love to see something like
viewport-dpi - the dpi
viewport-max - the maximum possible pixel dimension
and possibly viewport-current - the pixel dimensions at the time of the request
Decent responsive design should deal with the differing viewport sizes, but it might be nice to get a hint before delivering your page what direction to weight that response in.
Something like device-pixel-ratio would be more useful than DPI. Raw DPI is meaningless unless you take distance into account, as is very clear in the case of the projector.
viewport-dpi - the dpi viewport-max - the maximum possible pixel dimension and possibly viewport-current - the pixel dimensions at the time of the request
Decent responsive design should deal with the differing viewport sizes, but it might be nice to get a hint before delivering your page what direction to weight that response in.