I just updated my blog to WordPress 4.7.3, which was primarily a security update. As always I backed up my files and database first. I have automatic updates disabled so I can do this beforehand.
There was one slight problem with the update. My Facebook and Google+ share buttons on my posts quit showing, but only if I used the official buttons in Jetpack’s Sharing settings. It turns out that the Custom Tweaks for Jetpack plugin I was using to display the buttons on top of the posts was causing it. After disabling it, the buttons reappeared. I made a support thread in both the Jetpack and Custom Tweaks for Jetpack support forums. I may look for something else or just leave it as is.
So, other than this plugin conflict, everything else seems fine.
Update March 14, 2017: After Jetpack was updated to Version 4.7.1, the official buttons show again even with the Custom Tweaks for Jetpack plugin enabled. So, they changed something.