I'm running windows 8.1 with Visual Studio 2013 under IIS 7.5. When I just do the basic walkthrough to make sure everything works (and you have to change the configuration because the example configuration is for ClassicMode rather than Integrated Mode. I get this error message (same message dialog):

Unhandled exception at line 37, column 59140 in http://localhost:17127/9be8035d62004f708fdae3c9ff6146ac/browserLink

0x800a139e - JavaScript runtime error: Syntax error, unrecognized expression: div#ctl00$MainContent$NThinDiagramControl1

This appears to be a known problem on Connect but I have no idea how to get past it. Any ideas?
http://connect.microsoft.com/VisualStudio/feedback/details/805861/exception-when-visual-studio-2013-tries-to-setup-browserlink-connection-with-website-being-debugged-using-ie-11

Hi Jeff,

This looks like a bug in IE and it happens on a pre-release version of VS. We would recommend to do the development on a better tested configuration (like Win7 and VS 2012 / 2010).

Best Regards,
Nevron Support Team