Can my employer force me to sign away my right to dispute any errors in my current or past paychecks?

That form should not be valid or enfroceable against you. To be enforceable, a form or document must meet the criteria for a contract. One of the key criteria for a contract is that you must receive "consideration," or something of value in exchange for your promise (your promise to not dispute). But you are not receiving anything of value, because you have to be paid anyway: under both the labor laws and the principals of contract law (pertaining to the agreement, whether written or unwritten/oral, under which you work), if you worked, you MUST be paid. Paying you is not discretionary, and the employer cannot condition paying you the money you earned by working on your agreement to anything. So there is no consideration for the promise to not dispute, because you are receiving only the money to which you are entitled--and your employer must pay you--anyway. Without considertion, the "agreement" is not binding or enforceable. 
IF the employer gave you something extra to sign, that would be different--then that "extra" payment would equal consideration and make the agreement an enforceable contract. So say you earn $500/week, but the paycheck is for $510/week--the extra $10/week would be sufficient consideration to make the agreement valid. But you would have to get *something* beyond the pay you earned anyway.