The resolution we can obtain on a medium depends on the smallest part that can be used to represent a colour. Imagine a mosaic: the smaller the tiles the higher the possible resolution.
On photographic paper the minimum resolution depends on the smallest droplets of ink that can be deposited on the paper (inkjet, thermal, laser,….they use different techniques but for the sake of defining resolution we can stick to the droplets of ink…).
Resolution on video depends on the smallest size that a single pixel can have. Plasma has relatively bigger pixel size than LCD. This is why we don’t have plasma used in screen below 30”. 6 million pixels (what is needed for an HD TV- 2 million per red, blue and green) simply won’t fit.
New technologies like OLED and Nano Emissive Display (NED) can have much smaller pixel size (NED can be as small as 1/300 of an LCD and would be ok for delivering much higher resolution than today’s screen.
Although OLED technologies can increase resolution to over 150 dot per inch it is only with nanotech that we can get closer to paper resolution (we can reach 500 dots per inch, whilst with paper we can exceed 1000 dots per inch; however since our eye is not able to appreciate any resolution over 300 dots per inch we can say that nanotech would be indistinguishable to us from paper).
When will we see NED screens? The first screen based on this technology was a 5” prototype produced by Motorola in 2005.

Samsung and Sharp have been working on this technology, originally slated to appear on the mass market this year. Why it is not here as promised?
The reason is simple: the main motivation to produce NED screen was not resolution but lower production cost. The diffusion of LCDs and Plasma has driven cost down so much that this incentive is no longer there.
Higher resolution screens would be of interest to the market but we are missing the transmission technology that would bring content in Ultra High resolution to the screen.
Now the situation may change, thanks to multimegapixel digital camera but the market is too small, today, to convince video manufactures to invest billions of $ in this area.