I just purchased a motorcycle from a local dealer. It's a 2006 Honda CBR600f4i and its brand new! Now, ever the purchase on Tuesday, it has had problems. What are my return/exchange options! This is California so there is no cooling off period.

I would think your exchange options would be better than return because vehicles depreciate drastically as soon as they leave the floor. Since you have problems with it though they may not go according to depreciation value but exchange sounds more likely a win situation---as long as it the exchange doesn't have problems too.
I would let them know you are having problems asap and ask about your options.