Installation failing due to VC++ error(-2147023278)

First of all make sure you are running origin as admininistrator.

Secondly I would try to go to the "_installer/vc" folder in your BF4 beta folder and see if you can install VC++ manually or you need to repair your installation.

Also,

Welcome to the Battlefield 4 Beta Madness!

The beta is now in it's first stages and a lot will happen. ONE thing that will sadly not happen is that everything will go smooth. It's a beta, it's designed to find weak points and bugs so the launch of the real game will go smooth. You cannot expect a beta go smooth and everything to work, even if you payed extra to be in the beta.
You can expect all kind of problems like, beta not appearing, downloading, installing or starting. Servers, Battlelog, Origin etc. might also go down or be unstable.

Now, what you can do is:
-Wait! No reason to post questions about things not working if 1000 others have already done so.
-Search for solutions (using the handy dandy searchfields) on Battlelog and AnswersHQ (trust me, 2000 people had this problem before you did 😉 )
-Look at Twitter, Facebook, Google+. Battlelog and AnswersHQ for status updates from Battlefield
-Wait for EA and Dice people to identify and fix the problems as they occour
-Look at similar BF3 problems - it's the same engine, many solutions will be the same.
-Chillax, all good things come to those who wait 🙂
-Realise that you are not directly contacting EA, if you wanted to contact EA, even after reading all this and also knowing that the wait-time is going to be huge, then use the search bar to see how, there's a gazilion posts where it's mentioned.

Also: General information links:
General Beta Information: https://help.ea.com/uk/article/battlefield-4-beta-information
Exclusive Beta Information: https://help.ea.com/uk/article/battlefield-4-exclusive-beta-access-information
Battlefield 4 Premium Information: https://help.ea.com/uk/article/what-is-battlefield-4-premium
Battlefield 4 Preorder Information: https://help.ea.com/uk/article/battlefield-4-pre-order-overview
Preorder Code Redemption Issues: https://help.ea.com/article/battlefield-4-pre-order-code-redemption-issues
Beta Not Appearing Information: https://help.ea.com/article/battlefield-4-beta-preload-delay