WMG / Day of the Dead (1985)

Dr. Logan was both correct and incorrect when he stated that they were outnumbered by the zombies by 400,000-to-1.

He was correct, but only with regard to South Florida and perhaps Florida as a whole. Florida in the early 1980s had a population of 10-11 million people. However, much of Florida's growth and development has been due to technological innovations of the last hundred years or so. Without said technology and infrastructure, Florida would quickly become unlivable for the vast majority of the population. The collapse of society and the infrastructure along with it led to a mass die-off with the resulting famine, epidemics and social unrest likely killing more people than the zombies themselves. With everyone capable having long since fled the area, if not the whole state, it could very well be that the survivors in the movie are literally outnumbered 400,000-to-1 by the zombies.

However, that doesn't mean that the whole country, let along the whole world, would be in as dire a state. While it's mentioned that they've been trying to find other survivors using radio with no success, the equipment they have access to is old (according to McDermot, most of it dates back to World War II, and it had had little to no maintenance before the onset of the crisis) and the range is limited since all the radio relays on the mainland are offline, leaving them with only parts of southern Florida. Even then, there's no guarantee other survivors would have access to a radio themselves or electricity to power it. As it is, other regions in the United States and elsewhere are more habitable than Florida even without modern technology, so even though the living may well be outnumbered by the dead worldwide, it's very likely nowhere near as bad as it is in Florida and certain other places that were heavily populated before the apocalypse.

There was actual value in what Dr. Logan was doing, just in a way nobody thought of.

It's very clear that Bub holds an attachment to Logan, which is probably of the kind closer to Master/Dog than Father/Son. Bub also recognises objects, up to and including being able to fire a gun. He could easily have been used as some form of scout/supply runner, if his progress from just not biting Logan to being able to wield a gun (semi) accurately is a trend. With enough training, and the ability to replicate it, they could have just handed Bub a knife, stuck him at the gate and had him thin the horde somewhat. The long and short of it is that while Logan's research as a whole was useless towards the overall goal, there were potential uses for Bub.

The two Army zombies seen towards the end of the movie invading the complex originally belonged to Rhodes' unit.

It has been mentioned that six people had died since the Seminole Storage Facility was commandeered by the military, namely one scientist and five soldiers, the newest of whom was Major Cooper (though he was not buried, being used instead for experimentation by Dr. Logan). When looking at the graves, only two have helmets, indicating that there are at least 3 dead soldiers accounted for (with Major Cooper being an officer, he wouldn't have a helmet to represent him), so if there were four proper combat soldiers among the dead... where are the helmets of the other two? They're still on the heads of the now-undead soldiers who died outside the facility's gates trying to retrieve additional specimens for the science team.

Bub wasn't responding to the experiments because of the positive reinforcements.

Dr. Logan just kickstarted what was already happening, the zombies were getting smarter; as shown by Land of the Dead, the zombies were getting smarter all on their own, Bub just had help re-learning what he already knew.

Dr. Logan killed Major Cooper to run experiments on his corpse.

The film conspicuously does not tell us how Major Cooper died, only that he's dead, and that Logan swapped his body with one of the specimens. Logan's going off the deep end, and thinks nothing of feeding the already fallen soldiers to Bub. Either Logan killed Cooper, or arranged his death in such a way that he wouldn't be suspected, then swapped his body with one of the zombie specimens for burial.