A corrective patch and additional patch for Kingdom Hearts HD 1.5 + 2.5 ReMIX will be release on June 12, 2017 at 2:00 PM JST (5:00 AM GMT). Currently, there isn't information about what these patches will fix.
UPDATE 1: Details of the patches have been found. Theater Mode will be available for Kingdom Hearts Final Mix and Day 357 on Kingdom Hearts 358/2 Days will now have action scenes rather than just cutscenes. The Theater Mode patch will be 9.9 GB and Day 357 patch will be 353 MB.
UPDATE 2: The Day 357 and the Kingdom Hearts Final Mix Theater Mode add-ons are available in the PS Store for download. Europe and Australia appears to not have them yet. A game patch is also available. Version 1.03 includes fixes of the Kingdom Hearts II save glitch and Xemnas battle glitch along with a camera fix and better movement in Kingdom Hearts and Kingdom Hearts II among other fixes.
View an image of the additional Kingdom Hearts 358/2 Days cutscene and several images of the additional Kingdom Hearts Final Mix Theater Mode, thanks to the official Square Enix Blog, below:
Thanks to /u/Matthew0337 on Reddit for the screenshot of the patch details below:
UPDATE 3: The additional content is now available in Europe and Australia.