bootstrap multiselect dropdown width 100%

I used the buttonWidth parameter that .multiselect gives you similar to David Stutz. However, I put the '100%' right in the parameter.

<body>
    <select id="multiselect" multiple="multiple">
        <option value="1">Option 1</option>
        <option value="2">Option 2</option>
        <option value="3">Option 3</option>
    </select>

    <script type="text/javascript">
        $(document).ready(function() {
            $('#multiselect').multiselect({
                buttonWidth: '100%'
            });
        //caret is in the middle, switch it to right
        $(".caret").css('float', 'right');
        $(".caret").css('margin', '8px 0');
        });
    </script>
</body>

The below minimal example is working fine, so Bootstrap Multiselect is not override the styling. But note that in your case .dropdown-menu and .multiselect-container refer to the very same elements (the ul, like in the example below. So applying the styling to both classes, like you did is not necessary and may cause what you see in the inspector.

<!DOCTYPE html>
<html lang="en">
<head>
  <title>Bootstrap Example</title>
  <meta charset="utf-8">
  <meta name="viewport" content="width=device-width, initial-scale=1">
  <link rel="stylesheet" href="http://maxcdn.bootstrapcdn.com/bootstrap/3.3.6/css/bootstrap.min.css">
  <script src="https://ajax.googleapis.com/ajax/libs/jquery/1.12.4/jquery.min.js"></script>
  <script src="http://maxcdn.bootstrapcdn.com/bootstrap/3.3.6/js/bootstrap.min.js"></script>
<script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/bootstrap-multiselect/0.9.13/js/bootstrap-multiselect.js"></script>
<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/bootstrap-multiselect/0.9.13/css/bootstrap-multiselect.css" type="text/css"/>
<script type="text/javascript">
    $(document).ready(function() {
        $('#multiselect').multiselect({
            buttonWidth: '400px'
        });
    });
</script>
<style type="text/css">
    .multiselect-container {
        width: 100% !important;
    }
</style>
</head>
<body>
    <select id="multiselect" multiple="multiple">
        <option value="1">Option 1</option>
        <option value="2">Option 2</option>
        <option value="3">Option 3</option>
        <option value="4">Option 4</option>
        <option value="5">Option 5</option>
        <option value="6">Option 6</option>
    </select>
</body>
</html>