Good news! T-Mobile Tuesdays is working properly now. THANK YOU for being such awesome & patient Un-carrier customers! #GetThanked
— T-Mobile (@TMobile) June 7, 2016
Update (6/7/16 @ 7:35PM ET): T-Mobile says the servers are now ready for customers to make requests. CEO John Legere and COO Mike Sievert both said on Twitter that the company will “make it right” later this week.
Original Story (6/7/16 @ 12:32PM ET):

There's already a wave of problems for T-Mobile customers trying to claim their freebies for the first T-Mobile Tuesday.
Yesterday, T-Mobile Tuesdays was introduced during the Un-carrier 11 launch event in New York City. The program rewards customers with free gifts every Tuesday because the carrier wants to show just how much it loves the people that keep the lights on. In fact, Un-carrier 11 also includes Stock Up — an initiative to give customers a stake in the company by picking up one share for free. Between T-Mobile Tuesdays and Stock Up, I'm convinced this carrier really does appreciate its customers for growing the business and rattling the competition.
So many people are trying to claim free pizzas, movie tickets, Wendy's Frostys, and movie rentals that the servers are denying requests.

When receiving an activation code, the T-Mobile Tuesdays app is denying access after entry. The results are different, but I've been greeted repeatedly with a “500 Internal Server Error” message. Other T-Mobile customers are getting friendlier messages reading “There was an error attempting to contact the server.” No matter what the message is, a number of people are being locked out.
We'll have to wait and see if there's anything T-Mobile does to remedy the situation.
Source: T-Mobile, John Legere, Mike Sievert (Twitter)
https://www.youtube.com/watch?v=kjV_p7xWAM8
What a joke. Amatuers.