Volt Catfish being the game's electric-themed Maverick sounds like an odd idea, but real-life electric catfish do exist and might likely have been his inspiration.
Many are quick to point out that, despite Dr. Doppler ordering them to just capture X, the Nightmare Police will still kill X if they defeat him in the sub-boss rooms. Gameplay and Story Segregation aside, their personalities may be to blame here - Bit is a Professional Killer who brags about his head count, while Byte is a Blood Knight who loves to fight. It's possible that they get caught up in the moment and end up killing him instead.
Dr. Doppler's simple boss attack pattern is definitely in reference to his profession - formerly a Science Hero seeking peaceful resolutions to the Maverick problem, it would make sense that he is a Barrier Warrior with very simple and defensive strategies.
Bit, Vile MK-II, and even Sigma all have shields in X3 (though only one of them uses it). Flavor text in X DiVE and the Maverick Hunter Field Guide clarify that Bit and Vile choose to not use their shields in exchange for speed and aggression. Based on Dr. Doppler's Barrier Warrior moveset in his own boss fight, it appears he's trying to get his creations to use his favorite tool too.
The enemies that gave a base-level X the most trouble in the past were ones with strong defenses (Armored Armadillo, Vile's original Ride Armors, etc.). Doppler built his moveset by learning from those examples, which also explains the above fridge brilliance (he's trying to give them the edge over X). Sigma seems to have picked up on this too, fighting with a shield this time.
Vile is almost a total push over compared to his debut in Mega Man X but considering that X can actually destroy Vile's Ride Armor using only his buster, it would appear that Vile's technology may be falling behind. Also, because Dr. Doppler was the one who resurrected him, Vile's combat program was probably not upgraded to make him a modern war machine and Vile has a bad case of Artificial Stupidity as Vile may be assuming that this is the same X who couldn't even dent his Ride Armor and he's still a pushover.
Fans tend to act like Doppler's vaccine attack on Sigma was a total failure, considering he returns in future games, but was it really? Sigma doesn't use the virus at all in Mega Man X4, and when he uses it again in Mega Man X5 he dies from the stress and only comes back after being resurrected by Gate. Beyond X5, he never explicitly uses the Sigma Virus ever again - Gate made use of it to create the Nightmare, and fans assume it's how Sigma controlled Red Alert, but that's never outright stated. Maybe Doppler's vaccine was stronger than we thought, and left his virus permanently weakened. In-Universe, it's because Dr. Doppler, unlike Sigma who ran his rebellions with whatever resources he could capture, had all the resources necessary to speed up R&D at an even faster rate since Mega Man X2 because he's trying to build Sigma a perfect body.
It's pretty clear that the Cross Charge upgrade is less effective than the Double Charge upgrade. In the real world, Capcom probably noticed how broken the Double Charge was and changed the upgrade so players would use the Special Weapons instead of abusing the X-Buster, but provided the hidden Arm Chip or the mutually-exclusive Hyper Chip so that players could still count on it with the Hyper Charge ability. The Hyper Chip is an even better solution if you're willing to skip choosing a Chip as it also reduces the weapon energy consumption of the Hyper Charge.
How did Vile get his very own Kangaroo Ride Armor for his first battle? Well, the player unlocks the Ride Armor by freeing it from containment in the Weapons Factory Stage. It's likely that Dr. Doppler had already studied it and used its data to make one for Vile to pilot.
Look into the background of Doppler Stage 4 and you'll find rows upon rows of capsules containing bodies for Sigma. One shudders to think of what would've happened if X couldn't stop Dr. Doppler's plans.
Random Reploids can also be seen in the background of Doppler Stage 1. With how intent Doppler is on kidnapping X, it makes sense that he's kidnapping other advanced Reploids to use their bodies too.
Speaking of those Reploids. There's no evidence they escaped before Doppler's fortress blew up.
Dr. Doppler created a real vaccine to use on the Sigma Virus at the game's end. Depending on whether Zero is around or not, Doppler either installs it into his body or Zero uses it on his saber. The English and Japanese scripts differ on how Zero obtained it: the former says that Doppler gave it to him, while the latter says he found it while destroying the power core. If Doppler uses it, then Sigma may have hijacked his body long enough to escape in time. If Zero uses it, did he execute Doppler (US) or did Doppler die shortly after his boss fight (Japan)?
Listen closely to the ending where Doppler uses the vaccine - you can actually hear a second teleport sound after the explosions while the screen is white! That's how Sigma got away.
Remember those extra Sigma bodies mentioned above? Sigma uploaded himself to one to escape. The body he used in Mega Man Xtreme 2, which was styled after his body from Mega Man X2 body, could be that very body!
do exist and might likely have been his inspiration.