I usually walk on moving walkways, unless I'm with someone who stops then I will also but stand in front or behind them.

But I do have an issue with escalators. Bad knees (ankles, and back) here too, so I find escalators to be very awkward to walk on. The steps are a bit higher and wider than standard stairs. So I usually just stand on an escalator unless I'm feeling especially spry that day.

Oh, and escalators are the only situation where my left-handedness is a problem. I always carry things (purses, bags, laptop) on my right shoulder, and prefer to grab hand rails with my left hand. So I usually grab the left rail and then have to remind myself (or my harpy husband (LOL) reminds me a half second before I remind myself) to move over to the right.