So it seems that the PS3 version of the game, which was rumoured to have a 4 GB install, does not. In fact, the game only installs about 1 GB to the hard drive. Though the online component of the game (obviously not up yet) could require more. The alternate fatalities for the characters can be accessed by getting them from the Krypt. However, you can perform an alternate fatality without unlocking it in the Krypt. Once performed or unlocked  the fatality will show up in the character's pause menu move list. Additional costumes for the characters can also be unlocked in the Krypt along with concept art. Moreover, additional costumes can be obtained by beating the Arcade Ladder with a specific character (regardless of difficulty). Cyber Sub-Zero and Quan Chi can be unlocked by completing the story mode. It seems that you are awarded Cyber Sub-Zero after beating him in a match. Quan Chi is unlocked once the story mode is completed. 

Some of the details regarding the challenge tower have also been revealed. The first bit is that the tower consists of 300 unique challenges. Including one where you have to fight Goro who is able to instantly kill you with only a single hit. For that particular fight you have to use Sheeva. Interestingly the players on PS3Trophies note that Sheeva's stomp attack seems to break the game's AI by causing the characters its spammed on to remain on the ground taking damage. Also forget about playing as Shao Khan or Goro in this game as the bosses are only playable in the Tower. 

Also Klassic costumes and fatalities are not available within the Krypt probably because many of the Klassic costumes (for the ninjas at least) are being offered as DLC. This also seems to hint that down the line NetherRealms will release more Klassic costume and fatality DLC packs. Get those microtransactions ready, and strap 'em on!

Moreover, the Krypt contains 299 koffins to open. Some may note that this is less than the amount in Deception (which had 474). The difficulty within the game also scales as you win fights. If you start to get your ass handed to you over and over, the difficulty will scale back and give you a chance to win. 

If you've looked at the secret achievements/trophy list for this game 4 of the secrets are for unlocking hidden fights. These fights take place against super-powered characters within certain levels and even if you lose you will continue to progress up the ladder. One such fight is the 'Brotherhood of Shadow' achievement. Which is unlocked within this video (the begining of the video appears scratched up, but sit tight it does work):  

Here the player is in a stage called the Cathedral and after winning both rounds is treated to a fight against a powered up Noob Saibot.

Lastly, some of the Babalities have been revealed for a few characters. Babalities provide a higher Koin bonus and are all performed from jump distance. (the controls listed are for the PS3 version).

Sub-Zero - down back down circle
Kung Lao - down toward down triangle
Liu Kang - down down down circle
Cyrax - down forward back triangle