Vagueness is always an issue brought up in these cases. So is overbreadth. Those are merit-based arguments, not based on technicalities. Technicalities have more to do with, say, whether someone has standing to bring the lawsuit in the first place.
In the latter situations, courts must then decide whether someone does, in fact, have standing before they move on to the merits of the case (if the person does not have standing they almost always then jettison the case without deciding on the merits).
Alito, who concurred with the ruling, did so not because of the vagueness stated by Barry, but because he felt that the SCOTUS had already set precedent in striking down Nebraska's partial birth abortion ban. To him, it was the job of the court to follow SCOTUS precedent.
That's essentially correct.
Now SCOTUS struck down Nebraska, from what I gather here, due to lack of "life of the mother" exceptions and for entirely banning methods that could be used in non-partial birth abortion situations.
It should be noted, after the Nebraska case, SCOTUS accepted a partial-birth case from a different state & basically overturned its previous ruling.