You can’t open the application “LibreOffice.app” because PowerPC applications are no longer supported
Ensure that you're using the current version of it. If needed, delete and redownload it.
There has never been a PPC version of that application.
Boot in safe mode.* This will cause certain caches maintained by the system to be rebuilt. The instructions provided by Apple are as follows:
Safe mode is much slower to boot than normal.
When the login screen appears, reboot as usual (not in safe mode) and test. There's no need to log in while in safe mode.
*Note: If FileVault is enabled under OS X 10.7 or later, or if a firmware password is set, or if the boot volume is a software RAID, you can’t boot in safe mode.
Retrieving data ...