Recently, low-frequency, broad-band radio emission has been observed accompanying bright meteors by the Long Wavelength Array (LWA). The broad-band spectra between 20 and 60MHz were captured for several events, while the spectral index (dependence of flux density on frequency, with S-nu proportional to nu(alpha)) was estimated to be -4 +/- 1 during the peak of meteor afterglows. Here we present a survey of meteor emission and other transient events using the Murchison Wide Field Array (MWA) at 72-103 MHz. In our 322 h survey, down to a 5 sigma detection threshold of 3.5 Jy beam(-1), no transient candidates were identified as intrinsic emission from meteors. We derived an upper limit of -3.7 (95 per cent confidence limit) on the spectral index in our frequency range. We also report detections of other transient events, such as reflected FM broadcast signals from small satellites, conclusively demonstrating the ability of the MWA to detect and track space debris on scales as small as 0.1 m in low Earth orbits.