Last night beneath the moon...

The movement you though you observed of the planet was called autokinesis. Its where, if you stare at an object long enough, the muscles in your eye begin to twitch, thus giving the illusion that the object is waving back and forth.

Also, certain atmospheric conditions can bend light and make an object seem bigger and brighter than it really is. Mars has been visible for the past few months.

I myself am an experienced nightime sky watcher. What you described is pretty normal and common. I myself would only be curious if the aboject suddenly zipped across the sky in slience, or hovered in the same exact position the entire night, as planets and stars, because of earths rotation, rise and set.

Iv been watching mars and venus for the last month. I lost track of venus, but i watched mars move a little each night when it was right below the moon. A week or 2 ago about i saw an extremely bright object to the right and below the moon. It wasnt there on previous nights, as im an avid star gazer, i would have noticed. I looked at it through my binoculars and it was just an extremely bright white light, non-twinkling, and looked like two lights one on top of the other. I looked at other stars near the moon which were the usual blue to orange twinkling. But this one "star" was much brighter than the venus or mars I had been watching. Infact being white it was a totally different color than the plantes and stars. Cloud cover moved in over it which totally blocked it out.
I thought it was simply 'turned-off' because of its being at least as bright as to moon i thought i was odd it totally dissapered behind the thin clouds while the moon was still visible. (It definetly wasnt some tower or spot light by the way, it was sorta close to the horizen maybe 25° above it.)