I, too, am thinking of making a little network cable tester at some point. It would be comprised of two units, one to stick on each end of the cable (as the cable may already be placed up in the ceiling, through walls, and dropped down to another room). My only complaint about the low end ones currently on the market is that the master unit with the batteries and the switch is only a sender unit, you get no feedback. When you turn it on, you have to walk to the other room to get the results on the second unit, which consists only of red and green LEDs in opposing polarities.
I like your idea of using an LCD display. But the master unit with the power switch should be the one that displays the results. The other end should just be a plain closed passive connector. So far my idea is to use four pairs of opposing diodes, to determine if polarities are correct. There will also be specific resistors in series with the diodes, and each of the four pairs have a different value. That way when the 'brain' unit detects that yes in fact a signal is the correct polarity, it also has a way to use a voltage divider to see if it was the correct pair. Obviously sending out a signal on pins 1 and 2, and making it with correct polarity to the second unit on pins 7 and 8, should result in an error being detected back on unit 1.
The difficulty I'm having is that with the voltage divider, I'm wanting to have a sweet spot voltage range that only a pair with correct polarity in the correct order will produce. A crossover cable would have acceptable sweet spots too. Everything else would be thrown out into a "don't care" voltage range. The next logical step would be to look at every possible incorrect wiring situation, figure out the voltage level that would be read in that case, so the LCD can display exactly where the problem(s) are.