Pluto occultations are historically rare events, having been observed in 1988, 2002, 2006, and, as Pluto moves into the crowded Galactic plane, on several occasions in 2007. Here we present six results from our observations of the 2006 June 12 event from several sites in Australia and New Zealand. First, we show that Pluto's 2006 bulk atmospheric column abundance, as in 2002, is over twice the value measured in 1988, implying that nitrogen frost on Pluto's surface is 1.2-1.7 K warmer in 2006 than 1988 despite a 9% drop in incident solar flux. We measure a half-light shadow radius of 1216 ± 8.6 km in 2006, nominally larger than published values of 1213 ± 16 km measured in 2002. Given the current error bars, this latest half-light radius cannot discriminate between continued atmospheric growth or shrinkage, but it rules out several of the volatile transport scenarios modeled by Hansen & Paige. Second, we resolve spikes in the occultation light curve that are similar to those seen in 2002 and model the vertical temperature fluctuations that cause them. Third, we show that Pluto's upper atmosphere appears to hold a steady temperature of ~100 K, as predicted from the methane thermostat model, even at latitudes where the methane thermostat is inoperative. This implies that energy transport rates are faster than radiational cooling rates. Fourth, this occultation has provided the first significant detection of a non-isothermal temperature gradient in Pluto's upper atmosphere also reported by Elliot et al., possibly the result of CO gas in Pluto's upper atmosphere. Fifth, we show that a haze-only explanation for Pluto's light curve is extremely unlikely; a thermal inversion is necessary to explain the observed light curve. And sixth, we derive an upper limit for the haze optical depth of 0.0023 in the zenith direction at average CCD wavelengths.