I've noticed that quite frequently in Hell that when I kill an enemy that another will appear out of thin air without walking up to me, I'm not sure if it's a glitch that is spawning a copy of the foe or if the animation for approaching enemies is invisible to me. Not sure if others are getting this or if the glitch is just me.

It also occurs in the Nest

I have never seen this. What is your light radius? With sufficiently low radius, enemies will not be visible until they are very close.

I had this same issue, it was SUPER HARD. I was a Warrior lvl 33 and about 1/3 of the time when killing a demon, another exact copy would appear. It became a nightmare right in the Catacombs and Cave. I think it happened to me because i just moved my Diablo MP character into Hellfire and something must had got corrupted. I had to delete that character and start a fresh Hellfire character. Haven't had this issue since.

I had nothing affecting my light radius, I've had it make 4 or 5 copies of the knights in a row. Definitely a glitch somewhere, I've been playing the original copy of this game for almost 20 years, this is a new one for me. I didn't import the character from anywhere, this is my first character with a fresh unmodified install on this version of the game. I hope that if this is widespread the devs can tweak it. Not a huge issue for me gameplay wise, as long as the unique enemies don't start copying, like the Vizier.

The original developers are long gone. There will be no official tweaks. You aren't using a Doppelganger's weapon, are you? That is specifically designed to have a chance to duplicate enemies.

Scratch that, becoming a major hassle if it affects the power ranged units that flee and you're a warrior... had 3 lichs turn into 10, and that was just one room.

Oh! you nailed it, I have a doppelganger's sword. Never knew that was even a thing.

Doppelganger's is new in Hellfire. You cannot get it in Diablo. According to Jarulf's Guide, the prefix Doppelganger's has a 5% chance to duplicate an enemy.[1] However, this is a per-hit chance, so the more times you strike an enemy, the more opportunities you have to duplicate it. Thus, getting a new enemy 1/3 of the time is plausible if your damage is low enough that you required enough hits per enemy. Doppelganger's is only qlvl 11, and has statistics equal to a Lord's (qlvl 19) prefix. You should probably avoid using a Doppelganger's weapon if your enemies are still a meaningful challenge, since the duplication effect will just make the fight harder. Switching to a weapon with lower bonuses, but no negative side effects, might be a better choice overall. On the other hand, if you are able to comfortably win these battles, you could look at the duplicated enemies as opportunities for extra experience and drops.

Also according to Jarulf's Guide, Doppelganger's cannot duplicate unique enemies, such as The Vizier.

[1] Two places in the guide say 5% (3.13.5, page 60; 6.2.1, page 139). One place says 10% (3.4, page 25). I choose to believe the 5% note, particularly since one of those is a step-by-step translation of the combat code.