In that scene, Cooper's face is a "clock" telling us that time has stopped. If you look at it closely (it's easy to see when the background goes dark), it's not a freeze-frame of his face. There's movement, but it's on a little loop of one or two seconds. The face appears when Cooper notices Naido, disappears in the middle of him and Diane kissing, and then appears again when Cooper and Diane notice that the wall clock in the room is stuttering at 2:53 (that's when I realized what it was). It remains on screen until the scene cuts to the Great Northern boiler room where Cooper unlocks the door where the mysterious noise is coming from.
One interesting thing about Cooper's appearance in the sheriff's station is that for the onlookers, it was another David Bowie/Phillip Jefferies/Fire Walk With Me moment. Cooper showed up out of the blue, made time stop, said some cryptic things and then vanished.