I received my W-2 today, and should Box 1 on the W-2 be reduced by the pre-tax health insurance premiums I pay throughout the year? And if so the Wages, Tips, Compensation would be lower than the social security wages, and medicare wages in boxes 3 and 5, correct?

Yes, and no. Your federal wages reported in Box 1 is basically your wages minus pre-tax deductions for things like medical/dental insurance premiums, flex medical savings account, and 401(k) contributions. The wages reported in box 3 and 5 is basically your wages minus SOME of your pretax deductions, such as medical/dental but not 401(k) contributions. It may also include a few extra adders such as the cost of group life insurance that the company provides for you that is in excess of IRS guidelines. So for many people the amount in Box 3 or 5 may indeed be greater than in Box 1, but not because of pre-tax medical/dental insurance deductions.