I have experienced this many times, having bottled numerous batches, only to find that what I thought was crystal clear truly wasn't. Most times, there is just a fine sediment, such as you described. This I have never rebottled. I just pour delicately so as not to disturb the sediment, and advise friends and neighbors I give the occasional bottle to to do the same.
A couple of times, though, I have experienced a sediment that sits near the bottom, and looks for all the world like some kind of ethereal cotton. It never flattens out, but sits up a centimeter or two from the bottom of the bottle, like a ghostly fog enshrouding the "bump". To make matters worse, I have no idea where this wispy wickedness comes from, or how to prevent it. Perhaps others here have experienced this and could shed light on it. These, though, I have rebottled, just to make sure neither I nor anyone else had to deal with the hassle of pouring without disturbing this very delicate and naughty little precipitate.
Hope this helps. A life of meadmaking is truly a life of learning, so be sure to enjoy every lesson along the way! Good luck!