[Edit -6/9/2014] It appears that the adventure will only be inspired by B10 Night's Dark Terror and not actually include it. The actual adventure is Lost Mine of Phandelver. I didn't double check the information before I started writing and went off what I thought I heard rather than what was actually said. My apologies for misleading anyone.
Over the weekend it was announced that the module being used with the new edition's Starter Set is B10 Night's Dark Terror (which you can currently get for $4.99 in pdf). As an introductory adventure to showcase the new edition it's a good choice. The module takes place in a wilderness setting and is a great way to teach Dungeon Masters how to run one of the more difficult aspects of the game: wilderness encounters. Additionally, in the original module there were new charts for simulating weather conditions, new monsters, and 18 different adventure locations to explore which provided a vast array of opportunities for adventures that didn't occur in a 10 X 10 room with a single orc guarding a chest filled with rags and hate.
I never had the opportunity to play the original module when it was released but I did happen to find a copy a few years ago in a bargain bin at a local used bookstore, and looking through the adventure today I find myself intrigued by the idea of using this module for the new edition. There is a lot of potential for this module to provide my group with a far reaching and ever expanding arena to explore without locking them into a dungeon where their options are limited.
Without a doubt there will be changes made between the original edition and the one appearing in the Starter Set. Naturally the rules will be modified to reflect the differences in between the editions, but we can also expect the setting of the module to change. The original took place in Mystara, which given the current emphasis on the Forgotten Realms will almost certainly no longer be the case. But will that be the end of the changes for this module? Will Wizards expand their changes and alter more events within to reflect their Tyranny of the Dragons storyline? If they did would you even notice?