Anybody else update and then fail to open iTunes or Safari from icon?

First, ensure that you have current and complete backups of your apps and all of your data. (It seems that your environment might be corrupt.) First, boot into Safe Mode and try iTunes and Safari, and then reboot normally and see if that clears this misbehavior. Safe Mode rebuilds the boot-time caches, and that can sometimes clear odd issues. If not, If there are any anti-virus or security tools or cleaners, then test whether those tools are a factor by temporarily (or permanently) removing those from your system per the vendors' directions, reboot, and try again. If not, then see if downloading and installing the combo update for your particular macOS release works. (If you're running Sierra, here is the 10.12.6 combo.) Reinstalling the combo update for your particular release should not disrupt your apps and data. If none of that works, I'd probably boot from the recovery partition and reinstall — without wiping the disk — from there. But please have complete external backups before proceeding with any of this, whether created with Time Machine or otherwise...

Are you trying to open them from the Dock or the Applications folder? The Dock alias may be corrupt. If the Dock, try control - clicking the Dock icon, then Options, and uncheck keep in Dock. Then drag the application from the Applications folder to the Dock to create a new alias.

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