Okay, this is going to be a long one and highly analytic, so let's lay the groundrules. We're discussing organizational failures here, not individual mistakes.
Per the best study of the phenomenon I've found (It's called Military Misfortunes: The Anatomy of Failure in War if you care to look it up) military organizational failure is typically broken down into three modes: Failure to learn from the past, failure to anticipate the future, and failure to adapt to the present. From these three modes arise three types: simple failure, where you only screw up one way, aggregate failure, where you screw up two ways, and catastrophic failure, where you blow it in all three dimensions. Obviously, the more types of failure you combine, the worse the end result is. Simple failure is usually recoverable. Catastrophic failure is going to be decisive.
In The Great War, we have...
Failure to learn is irrevelant to the issue; there's nothing for anyone to learn from that has much bearing on the events that occur.
Failure to anticipate does not refer to an inability to peer into the future; nobody is clairvoyant. Rather, failure to anticipate is a failure to take precautions against a known threat. There is unfortunately a lot od this going around in the Great War.
The Vasudans failed to take precautions against the existence of the Lucifer. This is not wholly their fault, since they had neither time nor means to either destroy the Lucifer or disperse the population of their homeworld. However, it must still be ranked a failure as the existence of the Lucifer, its capablities, and the fact it was targeting Vasuda Prime were known in advance.
The Shivans got in on the action too, failing to take sufficent action to protect the Taranis from capture (a classic example in the end of a recovery), and failing to anticipate that the GTA and PVN would have many surprises to throw at them in terms of new equipment and tactics; each deployment of a new ship or new weapon didn't inspire them to prepare for the next one or behave more cautiously, even several fightercraft and many gun/missile models later. The Shivans should have realized at some point that they had hit the GTA in the midst of an upgrade cycle and made some kind of allowance for it, but they never did. The GTA was deploying a completely different weapons lineup at the end of the war from the one they had at the start with the exception of the Fury missile, and something similar apparently happened with the Vasudans.
The GTA alone is relatively blameless in this department; arguably the attack on Installation Riveria should be included here, but on the other hand a third-race situation was still too far out of context to be considered a "known threat".
Failure to adapt could be considered the story of the Shivan war machine, but for one significant fact; the Lucifer actually did change priorities. We know from the techroom at the beginning that it bombarded some random colony worlds. However once GTA and PVN resistance had stiffened sharply the Lucifer cut the crap and made a beeline for Vasuda Prime, then headed to Earth. This does not seem to have been standard procedure for the Shivans, if the Ancient's Monologues are to be believed; they killed everything and went for the homeworlds last. Similarily, Hellfire from Silent Threat offers tantalizing clues that the Shivans switched from their previous raiding tactics backed by annihilation of key points to a more conventional fleet-action based strategy after the Lucifer's loss. On the opposite hand, the Shivans never demonstrated adaptiblity on the battlefield; despite stiffening GTA/PVN resistence and a technological gap that closed very rapidly, Shivan tactics and deployment remained consistant throughout the war.
The GTA and PVN, by contrast, spent the entire war frantically adapting tactics and technology to combat the Shivans.
Proving the dictum that victory goes to the side which screws up least, the GTA and PVN commited only simple failure. The Shivans worked up to aggregate, and thus lost the Great War.
The Second Shivan Invasion is much more messy.
The GTVA drew lessons from the past, obviously. In the event, however, many of them proved unhelpful. This is not necessarily a failure to learn; there was no way they could have learned about the existence of the Sathanas design or the Sathanas fleet by studying The Great War. Positive lessons were learned and applied to GTVA ship and fightercraft design; AAA beams and flak cannon are almost certainly direct descendants of the discovery that shielded bombers rendered capital craft of The Great War desperately vunerable; the creation of the Artemis and Bakha bombers with their superior speeds and fighting qualities is outright stated to be the result of battle lessons.
Assessing if the Shivans learned anything is difficult. They too deployed AAA beams and flaks, but in numbers and placements suggesting more paying lip service to the lesson than actually learning it...but they continued to commit heavier numbers of fightercraft to escort duties, so there was not quite as much slack that needed picking up. They did however seem to grasp one lesson unequivocally, a similar one to one of the GTVA's: it is dodging the interceptor, not outlasting it, that gets ordnance to the target. This lesson is represented in the Nahema bomber. They also deployed the Mara fighter, which represents a significant departure from usual Shivan design standards of single-role fighters and a step towards the more multirole designs the GTA and PVN deployed in The Great War and the multirole craft the GTVA would deploy against the Shivans.
The NTF appears rather neutral on the subject; they were unable to deploy most of the more advanced craft from lessons learned in The Great War, but probably absorbed battle lessons from it. However at the end they almost certainly should have known the run to Gamma Draconis was suicidal from past experience.
Failures to anticipate are an interesting subject: the GTVA does not, in the final analysis, appear to have commited any such failures. In fact, the decision to evacuate Capella after the first Sathanas was sighted seems truly inspired in retrospect, considering the GTVA certainly had the means to take down one such ship. The existence of the Sathanas itself was not a predictable event; the existence of a whole fleet of them wasn't either.
The Shivans appear to have commited a single failure in this category; the first Sathanas was alone, and they should have reasonably been able to anticipate the GTVA could destroy such a ship if it was alone or lightly supported. Knowledge of the Colossus wasn't actually necessary for this conclusion; the GTVA had enough destroyers to do the job, and had a plan to do just that which they didn't get the chance to actually implement. The Shivans did learn from this, however.
The NTF commited the cardinal failures of anticipation; they started by extending into Deneb, and knowing that the GTVA had uncommited fleets and battlegroups that could easily rupture that front failed to take precautions against exactly what ended up happening. They also appear to have failed to take positive action to defend their fighter corps against the rising tide of the GTVA's second-generation fighters and new slew of weapons, all of which they would know of before the fact; the development of so many new fightercraft and weapons was by all indications already underway before the NTF seceded.
Failure to adapt is again, not apparently commited to the GTVA. They always had a reasonable, workable plan for their current circumstances. It may not have been pretty or a conventional definition of winning, but it was there.
The Shivans adapted their Sathanas deployment tactics to prevent further losses and that was the only pressing strategic concern requiring it. Of tactical concerns, they still were out there busily not adapting in the slightest. The end result is probably neutral.
The NTF, of course, failed to adapt to the Colossus' existence and to the changed circumstances it represented; their kamikaze run to Gamma Draconis symbolizes it. The bottom line was that the war was over, and every NTF crewer and pilot lost after the Colossus smashed the blockades into Polaris died without a purpose as far as we can tell. They failed to adapt ex post facto to the GTVA's second generation fighters and new weapons just as much as they failed to take measures against them before they arrived.
The Second Shivan Invasion demonstrates a different fundemental truth; when the material disparity is so great, screwing up just might not matter. The Shivans managed to reach aggregate failure again, while the GTVA made no mistakes at the organizational level; but it did not matter because there were 80+ Sathanas juggernauts and no GTVA counterforce. The Shivans could have dispatched their juggernauts into Capella singly at one-month intervals and that wouldn't have altered the end outcome in the slightest: the GTVA's forces would have been worn away to nothing before the Shivans had sent in half.
The NTF, by contrast, had no huge numerical advantage to fall back on and so paid the full price of reaching aggregate failure level: the loss of Polaris and the end of the NTF Rebellion as a political movement. The destruction the Neo-Terran Front as a meaningful fighting force occurred when they reached the level of catastrophic failure in the run to Gamma Draconis.
