When No Man's Sky was in development, developer Sean Murray made some vague suggestions as to how the game would work. When No Man's Sky was finally released, it turns out that a huge chunk of what was promised by Murray was found to be absent in the game. This, unsurprisingly, led to a huge uproar, with unsatisfied gamers ranting about the game and tanking the game's review scores across the internet.
However, things are about to get a lot more serious as it appears that the UK-based Advertising Standards Authority (ASA) will be launching an investigation on No Man's Sky and its promotional material surrounding the game prior to launch. A full list of claims that are currently being investigated has been posted on this Reddit thread, and judging from the list, it seems that the ASA will be comparing the final game to the demo that was previewed at E3 2014.
No one is quite sure as to what would happen should the ASA find Murray and the games development company Hello Games guilty of false advertising, however the ASA webpage does state that those who have committed false advertising will need to withdraw or amend their ads. If such is the case, the best case scenario will probably be Murray and Hello Games being forced to modify ads relating to No Man's Sky.