Layered transition metal dichalcogenides display a wide range of attractive physical and chemical properties and are potentially important for various device applications. Here we report the electronic transport and device properties of monolayer molybdenum disulphide grown by chemical vapour deposition. We show that these devices have the potential to suppress short channel effects and have high critical breakdown electric field. However, our study reveals that the electronic properties of these devices are at present severely limited by the presence of a significant amount of band tail trapping states. Through capacitance and ac conductance measurements, we systematically quantify the density-of-states and response time of these states. Because of the large amount of trapped charges, the measured effective mobility also leads to a large underestimation of the true band mobility and the potential of the material. Continual engineering efforts on improving the sample quality are needed for its potential applications.