I just bought a 3 inch 686 plus. When I load it up, the cylinder on the left side has some room so the round will move a little bit and rattles when the gun is moved. Is this normal? I don't see how it could be changed, but I thought it was odd there would be a round that could slide back and forth a little bit.

Be rest assured that it is completely normal.

My 686+ does it as well as my Ruger GP100.

Good to hear

That flare that allows the round to move is there to allow the cylinder pin to engage and push in until the cylinder is aligned. Take the rounds out and watch how the flare guides the pin inward as you close the cylinder.

By the way, with my first revolver I did the same double-take as well!