Executive Meddling: The reason why The Missing Link was DLC added later (rather than part of the core game, as originally intended) is because the game was rushed after being delayed repeatedly. This is the same explanation for the why the Tyrant boss battles are more "head-on" than series fans would've liked, since they were farmed out to third-party developers to save time during production (Which is also why two hub areas- Montreal and Upper Hengsha- were abandoned).
Fortunately, the Director's Cut puts everything back together (while maintaining the "separate but integral" feel of The Missing Link), and redesigns the boss battles to provide a much wider variety of options for dealing with them. Except the Hyron battle, which is completely unchanged.
Old Shame: Elias Toufexis, Adam's voice actor, claimed that he's embarrassed about some of the early recordings before he'd gotten a handle on Jensen's accent and speaking patterns, such as the conversation with Haas (which at certain points almost doesn't sound like Jensen at all). His explanation for the fluctuations is that the voice recording process took place over the course of two years and the resulting mix was between recent and old material.
Promoted Fanboy: Will Rossellini, the game's technical consulting for medicine and prosthetic, got the job because he reached out to Eidos saying how much his expertise could help the writing team, and because he was a huge fan of the original Deus Ex. The writing team in turn made him one of the employees in the Sariff offices, since he works in that field he would be present playing a Character as Himself. He thought this was awesome.
There were originally going to be more city hubs in the game: Upper Heng Sha (which was even partially completed), Montreal (the devlopers' home city, which they were rather regretful for not managing to include) and even India. They didn't complete these due to lack of development time, not wanting to stretch out the story too much and so that they could focus on making fewer but bigger hubs.
They also stated that the lack of development time was the reason why the game's ending is literally chosen via button presses as opposed to something more involved. The endings themselves however, were exactly what they intended.
A conversation boss fight with Megan Reed, that would have revealed more about their failed relationship.
An alternate opening, that had you breaking into Sarif HQ as to test their security system. The fact that you were breaking into Sarif and not a competitor firm wouldn't be revealed until the end of the sequence.
You were originally supposed to be able to spare Fedorova and Namir after defeating them. You can still see hints of the original idea in Eliza's conversation with Adam after the fight with Federova where she asks if you will save your opponent, dialogue that was never changed.
A cut level would have had you visit a Humanity Front rehabilitation clinic in Utah where people would have their augmentations removed. The rehab clinic would have secretly been home to a Purity First cell and was originally going to be where you had the social boss battle with Isaias Sandoval. The clinic was cut for time, but most of the completed content was moved to Detroit.
The Director's Cut reveals that Malik was originally intended to be Arabic and use Arabic swear words - while her VA could pronounce them right, the developers weren't happy and decided to change Malik into an American.
The Tai Yong Medical building was originally supposed to be arranged as a vertical factory, with a long shaft following the entire building and robotic production lines following the entire height of the building.
The Nigerian Emails that could be found throughout the game were originally collectables, with the player getting an achievement for finding them all. This was later cut.