I recently had delays installing SSMS 2016 and SSDT 2016 on certain Windows 7 machines. The installation would fail with error 0x80070643. The first time I go this error, I uninstalled all components that were modified that day related to SQL Server and was able to complete the installation on retry. It took about three hours.
The second time however, I narrowed the problem down to the Microsoft Visual C++ Redistributable. I uninstalled older versions of this component and was able to complete the SSMS 2016 installation successfully. The installer deployed the 2015 version of Microsoft Visual C++ Redistributable.
The install log can be found in a folder called SsmsSetup in the %TEMP% directory and the last error in the log file is typically.
Apply complete, result: 0x80070643, restart: None, ba requested restart: No