The More Information section of the Zero-Day release KB Article (2964358) contains some important information that you shouldn't miss. I say that because I've already seen community reported issues with the patch concerning Internet Explorer simply crashing or showing blank screens after the update is applied.
The More Information section clearly states…
Known issues with this security update
- Internet Explorer will crash if you try to install this security update on a Windows 7-based system that does not already have security update 2929437 installed. To avoid this issue, take either of the following actions:
- Install security update 2929437, and then install security update 2964358. For more information about security update 2929437, click the following article number to view the article in the Microsoft Knowledge Base: 2929437 Description of the security update for Internet Explorer 11 on Windows 7 and Windows Server 2008 R2: April 8, 2014
- Install security update 2964444 instead of security update 2964358. Security update 2964444 is intended for systems that do not have security update 2929437 installed.
P.S. I've also heard from community members that a similar issue is happening on Windows 8.x computers. There's currently no workaround for that, but I'll update you when one is available.