Uh no the dot pitch for LCDs just means the width and height of each pixel. So your typical 17" LCD monitor is:
1280 x 1024 pixels
337.92 mm wide x 270.336 mm high
=> dot pitch = 337.92 mm / 1280 = 270.336 mm / 1024 = 0.264 mm
A 19" LCD monitor is simply a larger 17" monitor, so it naturally has a higher dot pitch (each pixel is 0.294 mm on a side, so that's its dot pitch).
The dot pitch has nothing to do with the black space in between each pixel. For an LCD, the fundamental unit is a sub-pixel (a red, a green, and a blue sub-pixel make up a pixel), and the space in between each pixel is the same as the space in between each sub-pixel. This black space (which is where the transistor stuff and scan/data lines go) is simply limited by how thin the manufacturer wants to make those wires. So if you have a "screen door effect", it has nothing to do with the dot pitch but 1) looking at the monitor too close 2) manufacturer made those wires too wide.
The dot pitch on a 1600 x 1200 20.1" LCD is like 0.255 mm. That's roughly the limit of resolution of the eye at normal viewing distance, so it means you can barely make out text (usually one pixel thick) unless you work closer -- or you go blind trying to read. So unlike CRTs, a lower dot pitch for LCDs is not necessarily better.