Record-holder for biggest plot hole?

Yes, it did have a back up detonator.

But at the time the button failed, Tarek's handlers didn't know it had failed and only learned that later when he spoke to them on the mobile phone. By then, Tarek was not in a place that had the maximum casualties possible, so they didn't detonate after he explained that to them.

Then we saw them negotiate a new detonation time much later (skipping Saturday due to Shabbat and there not being as many people to hurt at the market).

Then later, when it was time again, his handlers were arguing over remote detonating, as one said they couldn't do it without "Tarek's permission."

Of course, in the end, nobody detonated but the bullet fired by the SWAT team set off the bomb.

It kind of showed the whole bizarre protocols involved in suicide bombers! It was really unsettling...