I have a Harbour Breeze Ceiling Fan that operates with a remote only. My problem is when you select the high mode, it appears to be running on low. What could be the problem?

WHat happens when you select other speeds?

Ceiling fan remote controls - help and FAQ- Ceiling Fans N More (http://www.ceiling-fans-n-more.com/ceiling-fan-remote-controls.php)

The other speeds appear to be extra slow as well.

Sounds like a bad capacitor. I presume it has no pullchains? In that case, usually the capacitor is in the receiver and the whole receiver has to be replaced.