A number of you raised good questions after class about the nature of procedural injuries and how they relate to standing. Let me try to clarify things a bit (though I'm happy to answer more questions).
First, a "procedural injury" is nothing more fancy than an injury that is tied, in some way, to the government's allegedly unlawful failure to follow a certain, legally required process. One can contrast a procedural injury with a direct harm in the following way. If the government illegally dumped toxic waste on your property, that would be a direct injury. If the government illegally failed to complete the required environmental impact statement before dumping toxic waste on your property, the injury would be "procedural" in the sense that the unlawful action was the failure to follow a certain process, and not the dumping of the toxic waste per se. (Indeed, after following the lawful process, it might be that the government could still dump the waste on your property.)
Second, why is this significant? Well, the basic point is that, if the Court did not relax the standing requirements to some extent for these so-called "procedural injuries," plaintiffs might lack standing to challenge a wide range of governmental action, despite being clearly affected by it. That is, in any case in which the allegedly unlawful conduct was the failure to follow a certain process--e.g., to initiate a rulemaking to consider whether carbon dioxide is a pollutant under the Clean Air Act, or to evaluate student applications without regard to race--the plaintiff would still have to show that, had the government followed the lawful process, the result would have been different. This is often quite difficult, if not impossible. How could Barbara Grutter, for instance, really have demonstrated that she would have been admitted to the Michigan Law School had the school not considered her race in evaluating her application?
Plaintiffs would thus lack standing to challenge all sorts of unlawful actions by the government. It is therefore significant that the Court has said that this is not necessary--that plaintiffs have standing when the procedural injury (the failure to follow a legally mandated process) is connected to an underlying injury in fact (denial of a subcontract, or loss of coastline, or whatever). So long as following the lawful procedure would make it more likely that the plaintiff would obtain the ultimate benefit (or avoid the ultimate harm), then the plaintiff has an injury in fact.
Third, it is worth reiterating that a procedural injury standing alone will be insufficient for purposes of Article III. It is not enough to assert that the government simply failed to follow the law. Such an "injury" is too abstract and widely shared. Rather, the alleged procedural injury must be connected to an underlying injury in fact that is both (a) concrete and particular, and (b) actual or imminent. This is why the procedural injury in Lujan was insufficient (it was not sufficiently imminent), but it was enough in Massachusetts v. EPA (because if the EPA did initiate rulemaking proceedings, it would be more likely that it would take steps to regulate CO2, which would in turn affect the state's coastal property).