Thermoelectric work by heat difference, I think in Australia your body would be the heat sink for a large part of the year! Snork.
A big problem with diodes is the voltage drop. As pointed out, 1mW into 50 ohms is only 0.6V peak, enough to turn on a germanium or shottky, but thereby wasting half the power. And a bridge rectifier doubles that drop.
Resonance boosts voltage, but at the expense of bandwidth.
Actually, there are a few projects going on where researchers are trying to use ambient RF fields to power a microcontroller, but they are -very- low power and spend most of their time storing energy, only coming on for a short time a few times a day.