angular-bootstrap 0.12.0 navbar dropdown not working

They added a uib-dropdown and uib-dropdown-toggle directive that you must use now. Here's your updated code snippet:

<div class="navbar navbar-inverse navbar-fixed-top" role="navigation" ng-controller="searchController">
    <div class="container-fluid">
            <div class="navbar-header">
            <button type="button" class="navbar-toggle" ng-init="navCollapsed = true" ng-click="navCollapsed = !navCollapsed">
                <span class="sr-only">Toggle navigation</span>
                <span class="icon-bar"></span>
                <span class="icon-bar"></span>
                <span class="icon-bar"></span>
            </button>
            <a ui-sref="dashboard" class="navbar-brand">My Application</a>
            </div>
            <ul class="nav navbar-nav navbar-right collapse navbar-collapse" collapse="navCollapsed" >
            <li ><a ui-sref="dashboard" ng-click="navCollapsed = true"><i class="fa fa-bullseye"></i> Dashboard</a></li>
            <li ><a ui-sref="topmenu1" ng-click="navCollapsed = true"><i class="fa fa-list"></i> Top Menu 1</a></li>
            <!-- Notice the dropdown directive -->
            <li class="dropdown" uib-dropdown>
                <!-- Notice the dropdown-toggle directive -->
                <a class="dropdown-toggle" data-toggle="dropdown" uib-dropdown-toggle>Dropdown
                    <span class="caret"></span>
                </a>
                <ul class="dropdown-menu">
                        <li><a ui-sref="item1">Item 1</a></li>
                        <li><a ui-sref="item2">Item 2</a></li>
                        <li><a ui-sref="item3">Item 3</a></li>
                </ul>
            </li>
            </ul>
    </div>
</div>

You can see some examples at http://angular-ui.github.io/bootstrap/#/dropdown

I think you are doing it wrong. What you are using is for Bootstrap and not UI-Bootstrap. Here is an example:

Template:

<div ng-controller="HeaderCtrl" class="navbar navbar-default navbar-static-top" role="navigation">
    <div class="container-fluid">
        <div class="navbar-header">
            <button type="button" class="navbar-toggle" ng-init="navCollapsed = true" ng-click="navCollapsed = !navCollapsed">
                <span class="sr-only">Toggle navigation</span>
                <i class="fa fa-bars"></i>
            </button>
            <a class="navbar-brand" href="#/home">Project Title</a>
        </div>
        <div class="navbar-collapse collapse" collapse="navCollapsed" ng-click="navCollapsed=true">
            <ul class="nav navbar-nav navbar-right">
                <li ng-class="{ active: isActive('/home') }"><a href="#/home">Home</a></li>
                <li ng-class="{ active: isActive('/about') }"><a href="#/about">About</a></li>
            </ul>
        </div>
    </div>
</div>

Controller:

var app = angular.module('controllers.header', ['ngRoute', 'ui.bootstrap']);

app.controller("HeaderCtrl", function($scope, $location) {

    $scope.isActive = function (viewLocation) {
        var active = (viewLocation === $location.path());
        return active;
    };

});

Have a look at this project: Angular Project Template. It's Angular 1.3, Bootstrap and UI Bootstrap. Exactly what you are trying to achieve.

Make sure everything is installed properly and that there are no errors in the console.