Issue 1:
[Bootstrap 3.0.3]

My html (cut through the body)

<body>
<nav class="navbar navbar-fixed-top navbar-inverse" role="navigation">
<!-- Brand and toggle get grouped for better mobile display -->
<div class="navbar-header">
<button type="button" class="navbar-toggle" data-toggle="collapse" data-target="#bs-example-navbar-collapse-1">
<span class="sr-only">Toggle navigation</span>
<span class="icon-bar"></span>
<span class="icon-bar"></span>
<span class="icon-bar"></span>
</button>
<a class="navbar-brand" href="#">Brand</a>
</div>

<!-- Collect the nav links, forms, and other content for toggling -->
<div class="collapse navbar-collapse" id="bs-example-navbar-collapse-1">
<ul class="nav navbar-nav">
<li class="active"><a href="#">Link</a></li>
<li><a href="#">Link</a></li>
<li class="dropdown">
<a href="#" class="dropdown-toggle" data-toggle="dropdown">Dropdown <b class="caret"></b></a>
<ul class="dropdown-menu">
<li><a href="#">Action</a></li>
<li><a href="#">Another action</a></li>
<li><a href="#">Something else here</a></li>
<li class="divider"></li>
<li><a href="#">Separated link</a></li>
<li class="divider"></li>
<li><a href="#">One more separated link</a></li>
</ul>
</li>
</ul>
<form class="navbar-form navbar-left" role="search">
<div class="form-group">
<input type="text" class="form-control" placeholder="Search">
</div>
<button type="submit" class="btn btn-default">Submit</button>
</form>
<ul class="nav navbar-nav navbar-right">
<li><a href="#">Link</a></li>
<li class="dropdown">
<a href="#" class="dropdown-toggle" data-toggle="dropdown">Dropdown <b class="caret"></b></a>
<ul class="dropdown-menu">
<li><a href="#">Action</a></li>
<li><a href="#">Another action</a></li>
<li><a href="#">Something else here</a></li>
<li class="divider"></li>
<li><a href="#">Separated link</a></li>
</ul>
</li>
</ul>
</div><!-- /.navbar-collapse -->
</nav>
</body>

Navbar fixed top that contain right alignment like an example seems to have no right padding.

It's close to browser border with no padding like the left alignment.

Navbar static top that contain right alignment seems to generate horizontal scrollbar.

example for navbar static top

<body>
<nav class="navbar navbar-static-top navbar-inverse" role="navigation">
<!-- Brand and toggle get grouped for better mobile display -->
<div class="navbar-header">
<button type="button" class="navbar-toggle" data-toggle="collapse" data-target="#bs-example-navbar-collapse-1">
<span class="sr-only">Toggle navigation</span>
<span class="icon-bar"></span>
<span class="icon-bar"></span>
<span class="icon-bar"></span>
</button>
<a class="navbar-brand" href="#">Brand</a>
</div>

<!-- Collect the nav links, forms, and other content for toggling -->
<div class="collapse navbar-collapse" id="bs-example-navbar-collapse-1">
<ul class="nav navbar-nav">
<li class="active"><a href="#">Link</a></li>
<li><a href="#">Link</a></li>
<li class="dropdown">
<a href="#" class="dropdown-toggle" data-toggle="dropdown">Dropdown <b class="caret"></b></a>
<ul class="dropdown-menu">
<li><a href="#">Action</a></li>
<li><a href="#">Another action</a></li>
<li><a href="#">Something else here</a></li>
<li class="divider"></li>
<li><a href="#">Separated link</a></li>
<li class="divider"></li>
<li><a href="#">One more separated link</a></li>
</ul>
</li>
</ul>
<form class="navbar-form navbar-left" role="search">
<div class="form-group">
<input type="text" class="form-control" placeholder="Search">
</div>
<button type="submit" class="btn btn-default">Submit</button>
</form>
<ul class="nav navbar-nav navbar-right">
<li><a href="#">Link</a></li>
<li class="dropdown">
<a href="#" class="dropdown-toggle" data-toggle="dropdown">Dropdown <b class="caret"></b></a>
<ul class="dropdown-menu">
<li><a href="#">Action</a></li>
<li><a href="#">Another action</a></li>
<li><a href="#">Something else here</a></li>
<li class="divider"></li>
<li><a href="#">Separated link</a></li>
</ul>
</li>
</ul>
</div><!-- /.navbar-collapse -->
</nav>
</body>

Issue 2:
The navbar right padding is broken when using navbar-fixed-top with Bootstrap 3.0.3.

Was working fine with Bootstrap 3.0.2.

navbar-static-top and navbar-fixed-bottom are probably impacted too.

Live example: http://plnkr.co/edit/zn1Pc0?p=preview

With navbar-fixed-top:

Without navbar-fixed-top:

The issue is most probably related to this commit: 5a03655

Version 3.0.3 contains the following code:

// Undo the collapse side padding for navbars with containers to ensure
// alignment of right-aligned contents.
.navbar-fixed-top &,
.navbar-static-top &,
.navbar-fixed-bottom & {
padding-left: 0;
padding-right: 0;
}

3.0.2 does not.