Person of Interest S02E09: Paid in "half"?

It's probably mostly artistic / dramatic licence.

From Reference.com

As of September 2014, torn dollar bills can be exchanged at any bank as long as more than one-half of the bill is still intact. If this is not the case, then the bill must be examined by the Bureau of Engraving and Printing

It is necessary to note a bill's approximate worth when sending it to the Bureau of Engraving and Printing. The bureau also requires a letter explaining how it was damaged. The damaged bill should be left in its original container, such as a purse or a box, to prevent further damage to the bill and help the investigator make a decision.

So would it be effective in real life? Probably not assuming the driver wanted to go through the hassle of going through the full procedure to claim the value but since this is payment for activity in an illegal event...he might just decide to go with the flow.

Note though that actually tearing a bill on half is illegal under Title 18, Section 333 of the United States Code.

Whoever mutilates, cuts, defaces, disfigures, or perforates, or unites or cements together, or does any other thing to any bank bill, draft, note, or other evidence of debt issued by any national banking association, or Federal Reserve bank, or the Federal Reserve System, with intent to render such bank bill, draft, note, or other evidence of debt unfit to be reissued, shall be fined under this title or imprisoned not more than six months, or both.