Examples of technicalities would be failure to Mirandize, a break in the chain of evidence (by criminal rules which were never designed to apply to a battlefield or to foreign LEOs), searches without warrants.
Do you honestly not see the difference between evidence from, say, Pakistan in the case of a terror suspect arrested in Pakistan, and one arrested in, say, Detroit? The detainees we're discussing mostly fall into three categories - detained by US or coalition military forces, detained by CIA assets, or detained by foreign civilian agencies. The first is not trained in civilian law enforcement and lives would be lost attempting to follow civilian law enforcement rules in a combat environment. The last is not trained in American civilian law enforcement procedures. The middle group may or may not have civilian law enforcement training, but are seldom in places or conditions where American civilian law enforcement procedures are practical. For instance, take a suspected terrorist nabbed by a CIA raid in Somalia. No US judge has jurisdiction to issue a search warrant. No Somalia judge would issue a search warrant. Your options are limited. Treat him like an American civilian and you can't touch him. Treat him like an enemy combatant and you can arrest and detain him, or kill him. If you choose to kill him, you lose any possible intelligence value and you lose the possibility to later decide he's possibly not guilty; can't release a dead guy. (Well, technically you can, but it's immaterial to the dead guy.) If you choose to arrest and detain him, you lose the chain of evidence necessary to proceed in civilian court. You simply cannot detach men from combat units to follow up, or to testify. You can't force informers to come to America to be faced in court. You can't force foreign actors military or otherwise to come to America to be faced in court.
If we choose to have military or foreign detainees to be tried in civilian criminal courts, we have the choice of either freeing them, or of establishing precedent that our legal rights are not necessarily important. If it's okay that Muhammed al-Sadr doesn't have the right to face his accuser in criminal court, why would Velvet Jones have that right? If Muhammed al-Sadr's house can be searched by government at will without a warrant, why not Biff McYuppy's house too?