When my bike was new I heard an irritating clicking (inconsistently) while on a ride. The friend I was riding with - a cycling veteran - was trying to help me figure out what it was: Bottom bracket? Slack from the chain? As I said above, all it turned out to be was a need to tighten the pedal. Just remember that to tighten the left pedal you must turn counter-clockwise, which is counter intuitive. Don't be afraid to give the wrench a light tap to ensure that the pedal is sufficiently tightened.

By the way, when the pedal clicked I would also feel the slightest bit of resistance and slippage from that pedal and that pedal alone, which sounds like your situation.