How does the SS dept know how much I make in any givin month?
Your employer reports your earnings to both the IRS and SS every time you get paid (although some companies might do this monthly or quarterly depending in their size). If you are self-employed, you'd be reporting that Quarterly when you file your quarterly taxes and make your normal quarterly contributions.
And yes, there are other drawbacks. If you start collecting at 62 your monthly benefit check amount is reduced. That amount will never go to the "full benefit" amount.
So if you are making $6k/month, your check size would be based on an "early retirement" amount and then they are going to reduce your check by $1 for every $2 you make. Do the math:
$6k/month x 12 months = $72k/year
$72k - $15,480 (the SS baseline) = $56,520.
$56.520/2 = $28,260.
So your SS benefits would be reduced by penalties of $28,260/year.... which is probably more than your SS retirement benefit amount will be to begin with.
The net effect of all of that would be that your would get a month SS check of $0 and at the same time, you'd be reducing the amount of your monthly SS check for the rest of your life.
All of that is to say, it is a horribly bad idea to file for SS at age 62 if you are going to continue working and making that much money. The entire idea of a "retirement" system is that you, ya know, actually retire.