If No Man's Sky has been less than stable for you, you'll want to download the game's latest patch, which promises to improve stability and add support for more hardware. The patch moves No Man's Sky up to version 1.04 and is available now on both PlayStation 4 and PC.
Additionally, Hello Games founder Sean Murray tweeted that the patch will improve frame rates on lower-specced gaming desktops. PC gamers can get the patch through Steam or GoG.
Murray tweeted that less than one percent of players have raised support issues, but 70 percent of issues would be fixed with this patch. He also suggested that the player base is very large, so one percent would be a lot of people. No official sales numbers for the game have been released, so it's hard to know just how many people Murray is talking about (For what its worth, the game is twelfth on the list of games being most played on Steam as of this writing, and that doesn't reflect PS4 players at all).
On Reddit, some PS4 players say they aren't seeing any changes in stability and that the game is crashing just as often as before and that number of glitches and exploits are still around. PC players seem to be enjoying more frames per second than they did before the patch.
Hopefully we'll get a better idea of what was changed when Hello Games releases official patch notes.