All of the US coins in 1965 1966 and 1967 were not minted in Philadelphia. None of them carry a mint mark, but they were produced at all 3 mints. They were trying to discourage hoarding, and people preferred the coins with mint marks, which were produced in lower quantities than Philly.
If they are still in the government holders it's pretty easy, at least for the 1965's. Out of the holders to some extent it is a guessing game and even the TPG's can't always tell. They have been know to slab coins right out of the sets as business strikes, and coins for OBW rolls as SMS. A typical business trike is pretty easy to tell, and a high end SMS is pretty easy to tell. But the difference between a high end business strike and lower end SMS can sometimes be anyones guess.
Good question. Philly made some. San Fran made sms ones with no mint mark, and Denver made some with no mint mark. My reference below states this and I always accepted that as "fact". I blame my ass for assuming it was correct. Post #13 and #15 are correct AFAIK. The pic in #13 is from a source I don't have, but there is a book I do have that says regarding 1965-1967... "The Denver mint also produced coins this year, however no mintmark was added so these are indistinguishable from the Philadelphia issues." pg 127, The Complete Guide to Washington Quarters, John Feigenbaum, 1994 softcover. I don't know where Feigenbaum got his info. I'll let you know if I find more. Maybe @Conder101 has a citation.
@green18 I found a bit of info in this article. His main reference I gather was the Annual Report of the Director of the Mint. https://www.ngccoin.com/news/article/711/
"The sole exceptions were the Special Mint Set coins, all five denominations of these ersatz proofs being minted at San Francisco"
What it means is you can't tell what mint a 1965 - 67 coins from with the exception of the coins in the SMS sets which were all struck at San Francisco.
I used to have some '65, '66, and '67 P, D, and S but I couldn't prove where they came from so I just spent most of them. I don't even remember all the ways I knew after all these years. Some were just the point at which they were released but there was some documentation on some as well. Once a coin with no MM leaves a mint it doesn't matter much anyway.