in the NIST Curve arena, I think DJB's main concern is engineering implementation - from an online slide deck he published:
We’re writing a document “Security dangers of the NIST curves”
Focus on the prime-field NIST curves
DLP news relevant to these curves? No
DLP on these curves seems really hard
So what’s the problem?
Answer: If you implement the NIST curves, chances are you’re doing it wrong
Your code produces incorrect results for some rare curve points
Your code leaks secret data when the input isn’t a curve point
Your code leaks secret data through branch timing
Your code leaks secret data through cache timing
Even more trouble in smart cards: power, EM, etc.
Theoretically possible to do it right, but very hard
Can anyone show us software for the NIST curves done right?
As to whether or not the NSA is a strategic adversary to some people using ECC curves, I think that's right in the mandate of the org, no? If a current standard is super hard to implement, and theoretically strong at the same time, that has to make someone happy on a red team. At least, it would make me happy, if I were on such a red team.