The mission to the mass of ships-turned-base full of brute scavengers in EF1, but most particularly the section that takes place onboard a mirror universe constitution class starship.
"Virtual Voyager" from the first game is often thought of very highly, as it essentially replicates the entirety of the ship for players to run around in. There are mini-missions to complete, hidden areas, weapons and collectibles to find, and all sorts of entertainingways to cause chaos and death.
Goddamned Bats: The Harvesters, Antibodies and Parasites in EF1; the Exomorph Lurkers and Chewers in EF2.
Hell Is That Noise: The mission to the Dallas in the second game. The noises of Exomorphs when they aren't even attacking you at that point. The dramatic strings in the music don't help at all.
A more subtle example is the metallic scream enemies make when they're vaporized by a phaser or compression rifle. Even the female characters make the noise too.
Les Yay: In EF1, if you play as the female Munro, the flirting between Munro and Telsia doesn't change at all, making it rather unfortunate that you could not play as a female Munro in EF2.
Porting Disaster: The PS2 version of EF1 was not as well received as its PC counterpart.
That One Level: The introduction level can be this for some. Specifically, the part where you're supposed to "escape a Borg cube." It's a holodeck simulation, but it still manages to be ludicrously difficult for those who aren't familiar with Voyager.