My CD player occasionally refuses to auto-inject a CD, and I've got to eject and re-insert a few times.
If your CD player is skipping, try using a Cd lens cleaner disc. These are available at most stereo stores, and they've saved my butt once or twice. Typically, it's just a CD platter with a tiny soft brush on the underside that wipes dust from the lens. You may want to try this before replacing the head unit.
-D