Application_Error in global.asax not catching errors in WebAPI

Abstract out your error handling logic from Application_Error into its own function. Create a Web API exception filter.

//register your filter with Web API pipeline
//this belongs in the Application_Start event in Global Application Handler class (global.asax)
//or some other location that runs on startup
GlobalConfiguration.Configuration.Filters.Add(new LogExceptionFilterAttribute());

//Create filter
public class LogExceptionFilterAttribute : ExceptionFilterAttribute 
{
    public override void OnException(HttpActionExecutedContext context)
    {
        ErrorLogService.LogError(context.Exception);
    }
}

//in global.asax or global.asax.cs
protected void Application_Error(object sender, EventArgs e)
{
    Exception ex = Server.GetLastError();
    ErrorLogService.LogError(ex);
} 

//common service to be used for logging errors
public static class ErrorLogService
{
    public static void LogError(Exception ex)
    {
        //Email developers, call fire department, log to database etc.
    }
}

Errors from Web API do not trigger the Application_Error event. But we can create an exception filter and register it to handle the errors. Also see Global Error Handling in ASP.NET Web API 2.