warmth = the warp your record acquires when it gets warm. Mild warp (warmth) means the sound speeds up and slows down as it rides the hills and valleys. More warp (warmth) is the gap in sound as the needle achieves that coveted liftoff effect. "Warmth" can also happen when the manufacturer punches the center hole off-center, a depressingly common characteristic. Also known as "Doppler shift".
Depth = when the grooves are too close together and exceed a certain depth, you can simultaneously time travel both forwards and backwards in the music by about 2 seconds. This quantum "depth" effect is most prized.
Those are just artefacts that vinyl provides. As digital is a superior format, technically, it would be possible to record/produce/mix a song to sound identically (flawed) to vinyl.