Black tower is one of the strangest places in the main series games. Its effectively the Mount Battle/Battle Tower alternative to the Gen 5 games, but with a much more uneasy atmosphere and very malicious trainers.
>Color scheme
Every few areas, the color scheme of the floor and ceiling change to match one of the colors of the original 4 pokemon games. While this isnt as concrete, I find it worth mentioning because the two most important areas in the building: the lobby and final floors, sport the colors of team rocket (black and red).
>Cloned/manmade pokemon and trainers
Team rocket has a history of trying to clone pokemon, such as mew, for their own purposes, and its not uncommon to meet the same trainers over and over again as you progress through the tower, though they act as if they've never met you before and several of them are assigned to work on earlier floors. Porygon-Z is a commonly reoccurring pokemon in the mid level, and Team rocket is hinted at having some part in the creation of PGZ, and having attempted to take over Silph co because Porygon are capable of traveling to alien dimensions. Theres also several legendary pokemon that do not make sense being here.
>Giovanni is in Unova
Giovanni shows up to battle in the PWT despite being a wanted man that is no longer considered a gym leader.
>Black tower is from an alternate reality
The story behind Black Tower is incredibly odd. Several NPC's mention that the tower just appeared one day out of the blue, and nobody has any idea who owns it
>Data analysis
The staff of the tower are incredibly secretive, and are mentioned to analyze Pokemon Battles to collect some kind of data. Why is this relevant, you may be asking? A majority of the trainers you find in this place are children and teenagers/young adults around Red and Gold's age when they beat team rocket. Team Rocket are looking for training prodigies like Red by hosting this battle tower to understand the mindset and strategies of powerful trainers