Otto Zander, the "main character" in Guavamoment'sX-COM Let's Play, was made into an X-COM hero unit in the remake.
Many fans of the original X-Com loved to exaggerate the threat of Chryssalids, with several Let's Play retellings deliberately including missions where X-Com is forced to face massive numbers of Chryssalids, most notably Guava's LP where Japan is overrun. The Enemy Within Council Mission "Site Recon" plays out almost exactly like some of them, even allowing for the possibility of operatives failing to reach the evac point by the time bombs start dropping!
In Enemy Within, one clue you can get to the location of EXALT's HQ is that they are based in a country you can play as in Civilization V, which is also developed by Firaxis.
Doing It for the Art: Lead designer Jake Solomon has been an enormous fan of the X-COM franchise since he was a child, and as this article reveals, it's no understatement to say that his journey to create Enemy Unknown was nothing short of a lifelong passion.
Code Black: Refers to a failed mission where all your operatives got horribly murdered by aliens or EXALT.
C-Hive, C-Day: C-Day refers to the first time you encounter Chryssalids, an old term inherited from the original X-Com fandom. C-Hive refers to the Chryssalid 'hive' aboard the fishing vessel in the Council Mission Site Recon. Sometimes Site Recon itself can be addressed as C-Day on its own.
Thin Mints: Thin Men deliberately misspelled.
Eggsalt: EXALT also deliberately misspelled, the salt part probably appropriated from the salty meme and EXALT's tendency to Zerg Rush players remorselessly which'll probably make every loss to them feel kinda cheap.
Crit Men: An infamous nickname for Thin Men from higher difficulties, where players find them distressingly accurate.
Ayy: Sectoids, appropriated from the ayy lmao meme.
FUTBOL: Muton squads, as popularized by Youtube and Twitch streamer Beaglerush.
Pretty much everyone on the development team adored the original. Enforced for those who hadn't played it before; every other Friday, time was set aside to play the original. All of them became addicted.
A story Quentin Smith of the "Sit Down and Play" site told was that in the early stages of development, the developers couldn't figure out how the new XCOM was supposed to play. So they went to the house of Sid Meier and used dice, paper and wooden tokens as a bare-bones XCOM to get a feel of it. An XCOM board game... Wouldn't you wanna get your friends around a table to give it a shot?
Originally, the Muton was supposed to get a mechanical variant in Enemy Within instead of the Sectoid, but was looked over due to already being big.
The base ini file suggests there were as many as 36 nations on the Council before it was pared down to 16. The remnants of this can be seen in the appearance of nationalities among recruited soldiers not on the Council such as the Netherlands, Sweden, and South Korea.
Prestige Classes were considered for inclusion in Operation Slingshot, including the Flame Trooper for Assault classes. They would be unlocked through special missions that would be identical between playthroughs.
There is proof of concept footage of significantly more dynamically-animated combat for XCOM: Enemy Unknown, almost looking like Gears of War turned into a turn-based tactics game with the units constantly moving in their square to exchange fire and duck (a bit like the animations of units inflicting or receiving Suppression), and the senior soldier ordering the junior. Also, a soldier gets injured and grips himself in light of that as well as visibly reacting with horror to his comrade being killed. Lastly, the ending shows a soldier having killed a Muton with his knife, making it obvious the use of melee combat for XCOM was considered before it actually happened in 2.