Does my son need to file a return if he is a college student and received funds from a 529 set up by his grandparents? He does not work so would not otherwise file.

Q. Does my son need to file a return if he is a college student and received funds from a 529 set up by his grandparents?

A. Simple answer: No.  

Q. Who reports the amount listed on the 1099-Q - his grandparents, us (his parents), or my son (the student)?

A. Most likely nobody. If it does need to be reported, the person shown on the 1099-Q, as the "recipient" reports it. That person's SS# will be on the 1099-Q.

On form 1099-Q, instructions to the recipient reads: "Nontaxable distributions from CESAs and QTPs are not required to be reported on your income tax return. You must determine the taxability of any distribution." 

See the discussion below for details.

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Qualified Tuition Plans  (QTP 529 Plans)

It’s complicated.

For 529 plans, there is an “owner” (in this case the grandparent), and a “beneficiary” ( the student ). The "recipient" of the distribution can be either the owner or the beneficiary depending on who the money was sent to. When the money goes directly from the Qualified Tuition Plan (QTP) to the school, the student is the "recipient". The distribution will be reported on IRS form 1099-Q. 
The 1099-Q gets reported on the recipient's return.** The recipient's name & SS# will be on the 1099-Q.
Even though the 1099-Q is going on the student's return, the 1098-T should go on the parent's return, so you can claim the education credit. You can do this because he is your dependent.

There needs to be some coordination between the parent (assuming the student is your dependent) and the recipient. You can and should claim the tuition credit before the grandparent (or student) claims the 529 plan earnings exclusion. The educational expenses they claim for the 1099-Q should be reduced by the amount of educational expenses you claim for the credit.
Be aware, you can not double dip. You cannot count the same tuition money, for the tuition credit,  that gets him an exclusion from the taxability of the earnings (interest) on the 529 plan. Since the credit is more generous; use as much of the tuition as is needed for the credit and the rest for the interest exclusion. Another special rule allows you to claim the tuition credit even though it was "his" money that paid the tuition.
In addition, there is another rule that says the 10% penalty is waived if he was unable to cover the 529 plan withdrawal with educational expenses either because he got scholarships or the expenses were used (by him or the parents) to claim the credits. He'll have to pay tax on the earnings, at his lower tax rate (subject to the “kiddie tax”), but not the penalty.

Total qualified expenses (including room & board) less amounts paid by scholarship less amounts used to claim the Tuition credit equals the amount you can use to claim the earnings exclusion on the 1099-Q. 
Example:
  $10,000 in educational expenses(including room & board)

   -$3000 paid by tax free scholarship***

   -$4000 used to claim the American Opportunity credit (on the parent's return)

 =$3000 Can be used against the 1099-Q (usually on the student’s return)

Box 1 of the 1099-Q is $5000

Box 2 is $600

3000/5000=60% of the earnings are tax free

60%x600= $360

The recipient has $240 of taxable income (600-360)

**Alternatively; you can just not report the 1099-Q, at all, if the student-beneficiary has sufficient educational expenses, including room & board (even if he lives at home) to cover the distribution. You would still have to do the math to see if there were enough expenses left over for you to claim the tuition credit. Again, you cannot double dip!  When the box 1 amount on form 1099-Q is fully covered by expenses, TurboTax will enter nothing about the 1099-Q on the actual tax forms. But, it will prepare a 1099-Q worksheet for your records, in case of an IRS inquiry.

 ***Another alternative is have the student report some of his scholarship as taxable income, to free up some expenses for the 1099-Q and/or tuition credit.

On form 1099-Q, instructions to the recipient reads: "Nontaxable distributions from CESAs and QTPs are not required to be reported on your income tax return. You must determine the taxability of any distribution."