I moved to Korea in July of 2010. I have a year contract which I fully expect and intend to complete, but at this point I have only been out of the country for 6 months. Does that mean I cannot apply the foreign earned income tax exclusion to my 2010 tax return (because I haven't been gone for 330 consecutive days yet)and I will have to pay taxes on the money I earned last year in Korea? But I will be able to apply it to my 2011 tax return, after I have finished my 12 consecutive months/330 days? If that is the case, will it matter that I have already paid taxes on income earned during the first 5 months of that 12 month period?

On Form 2555 you must put dates for you physical presence test. So file only after you complete the test. Your U.S. Tax Return: U.S. Citizen or Resident with Foreign Income

You should file an extension of time to file (Form 4868) until you meet the test, and then file your 1040 claiming the exclusion you are entitled to for 2010 based on the calculations on Form 2555 as previously noted.