Driven by the incomplete understanding of the formation of gas giant extrasolar planets and of their mass-radius relationship, several ground-based, wide-field photometric campaigns are searching the skies for new transiting extrasolar gas giants. As part of the Trans-atlantic Exoplanet Survey (TrES), in 2003/2004 we monitored approximately 30,000 stars (9.5<=V<=15.5) in a 5.7deg×5.7deg field in Andromeda with three telescopes over 5 months. We identified six candidate transiting planets from the stellar light curves. From subsequent follow-up observations we rejected each of these as an astrophysical false positive, i.e., a stellar system containing an eclipsing binary, whose light curve mimics that of a Jupiter-sized planet transiting a Sunlike star. We discuss here the procedures followed by the TrES team to reject false positives from our list of candidate transiting hot Jupiters. We present these candidates as early examples of the various types of astrophysical false positives found in the TrES campaign, and discuss what we learned from the analysis.