The NIST document specifying Dual EC offers default values for each curve. P is the usual base point for the curve; an arbitrary point Q is provided without justification or details of its generation.
Because the NIST curves have cofactor 1, all points other than the identity generate the same subgroup. This means any two points P and Q are related by some scalar d such that d * P = Q. Knowledge of d is the back door in the generator.
This also implies a simple means for choosing Q given P: pick a random integer d and calculate Q = d * P. Publish P and Q and then write down d someplace safe. This is exactly how NSA is speculated to have chosen the Dual EC parameters.
However, the NIST document also specifies a method for generating alternative points. It boils down to hashing a random seed and mapping the result to a curve point. If you generate the base points P and Q like this, the relationship between them is unknown. The scalar d still exists, but now no one knows what it is. Without that knowledge, there is no back door.
It's not clear from that page how Juniper chose the parameters. Maybe they did choose a random scalar and multiply P, or maybe they followed the standard. The information on that page isn't enough to say one way or the other.
EDIT: Just to be clear, I'm not saying this isn't something to worry about. You should distrust and avoid anything that relies on Dual EC. I'm only saying there is not enough information to say definitively that Juniper put a back door in their own product, intentionally or otherwise.
The NIST document specifying Dual EC offers default values for each curve. P is the usual base point for the curve; an arbitrary point Q is provided without justification or details of its generation.
Because the NIST curves have cofactor 1, all points other than the identity generate the same subgroup. This means any two points P and Q are related by some scalar d such that d * P = Q. Knowledge of d is the back door in the generator.
This also implies a simple means for choosing Q given P: pick a random integer d and calculate Q = d * P. Publish P and Q and then write down d someplace safe. This is exactly how NSA is speculated to have chosen the Dual EC parameters.
However, the NIST document also specifies a method for generating alternative points. It boils down to hashing a random seed and mapping the result to a curve point. If you generate the base points P and Q like this, the relationship between them is unknown. The scalar d still exists, but now no one knows what it is. Without that knowledge, there is no back door.
It's not clear from that page how Juniper chose the parameters. Maybe they did choose a random scalar and multiply P, or maybe they followed the standard. The information on that page isn't enough to say one way or the other.
EDIT: Just to be clear, I'm not saying this isn't something to worry about. You should distrust and avoid anything that relies on Dual EC. I'm only saying there is not enough information to say definitively that Juniper put a back door in their own product, intentionally or otherwise.