This answer record lists the known issues for the Installer in the Vivado 2013.x releases.
Each known issue includes a link to another answer record that contains additional information on the issue.
Outstanding Issues in Vivado 2013.4
Resolved Issues in Vivado 2013.4
(Xilinx Answer 58521) - 2013.3 Install - DocNav fails to install
Resolved Issues in Vivado 2013.3
Resolved Issues in Vivado 2013.2