A dancing signal strength bar, to me, indicates a possible multipath problem. It is more noticeable on windy days when tree branches and your antenna sway back and forth.
In the analog days, you would have seen ghosting or a fading/shaking picture as the reception constantly changes or bounces off metal objects. If the problem was interference from another station on the same channel, you would have seen a ghosting image from the interfering station drift across the screen, flashing and/or shivering if severe. (The flashing in the digital era would also cause the bar to dance as the interfering signal is rapidly fluctuating).
HD Radio: An Audiophile's Worst Nightmare.