I just installed a new Hunter fan (the Canadiana - Model 27545).

The fan has three speed settings (High, Medium, Low) as well as an "off" option.

With the fan set to "Medium", the lights are at their brightest.
With the fan set to "High" or "Low", the lights get dim.
With the fan set to "off", the lights are brighter than "high" or "low" but still dimmer than "medium".

Anyone know what's going on?

Ok. This is lame but I will answer my own question.

The problem was one of the light bulbs was not screwed in properly. The bulb was put in (by my wife) at an angle and not all the way in. I believe that the improper connection was causing a short which was affecting the lighting levels with respect to varying fan speeds.

Almost sounded like a loose neutral/white wire.