The new patch adds LAA support that means if you also use a 4GB patch, you could be patching the same thing twice, and the second one may be undoing what the first one did

Disable your 3rd party 4GB or LAA patches before trying to run. If you use a custom launcher in NMM, remove it also until you have tested the game and see if it is still needed - especially if your custom launch includes a 4GB patch.
Any mods that require other 3rd party extensions - such as SKSE or Dragon Script - those will no longer work until a new version is made for the new version of Skyrim. And if you are launching using them, it could cause a crash. Disable them until a new version is released (Note: a new version of SKSE is already out)
For those who didn't know, or possibly forgot. A new game patch MAY (and probably does) replace any custom Skyrim.ini and SkyrimPrefs.ini changes you made with the default unmodified versions - Using a backup may not work as they may have made some changes in the ini files also. Instead, compare the new with your backup to see what needs to be changed.
Any changes you made in the controls etc to make your game work better - such as mouse acceleration MAY be affected or changed by the patch. If so, you will have to reapply those changes.
This is NOT a bad thing or something EVIL by Beth, it is common sense. They don't know what you have and how the new patch will affect what you have, so they patch to factory spec only, leaving it up to you to put back any changes you made to the game that change it from the default settings. Make backup copies of things like the modified ini files, Skyrim.exe and other things that could be changed by future game patches.