Just had Aloha Breeze 52" ceiling fan installed as hugger mount in family room. The part that is rocking back and forth is the area below the blades and inside the main motor housing. There is a single light fixture below that.
Wobbling is worse at the higher speed, of course. Installer was puzzled why, when he took the pieces out of the box, there was a lot of play in the housing.
Did we miss installing a couple stabalizing screws? Thanks.

You can try balancing the blades.

Ceiling fan blade balancing issues - Ceiling Fans N More (http://www.ceiling-fans-n-more.com/blade-balancing-issues.php)

But Aloha Breeze is a very cheap ceiling fan. Return it and get something decent.

Returned it and installed a Hunter brand. Very nice. Very stable. Thanks for your response.

I recommend Hunter. Nice going!