I've added a Facebook and Google+ icons to the header with the following code to the Custom Header:

<!-- AddThis Follow BEGIN -->
<div id=AddThisBox>
<div class="addthis_toolbox addthis_default_style">
<a class="addthis_button_facebook_follow" addthis:userid="andrewthomas.0"></a>
<a class="addthis_button_google_follow" addthis:userid="106721125817540228206"></a>
</div>
<script type="text/javascript" src="http://s7.addthis.com/js/300/addthis_widget.js#pubid=xa-50856f25664510e6"></script>
<!-- AddThis Follow END -->
</div>

And the following code to the CSS:

#AddThisBox {
position: relative;
float: right;
padding-top: 35px;
padding-right: 20px;
}

All looks good on the homepage but within the gallery the icons are no longer in the header. Also, in the Galleries page, the icons are in the correct position but they move when the page is scrolled.

Can someone please help me get the icons to stay in place?

Instead of this in your CSS:

#AddThisBox {
position: relative;
float: right;
padding-top: 35px;
padding-right: 20px;
}

Use this:

#AddThisBox {
position: absolute;
top: 35px;
right: 20px;
}

Thanks Eric

On my Galleries page (that is made from a duplicate homepage) the social icons move when the vertical scrollbar is moved. Any idea how to fix this?

I'm not seeing them move on this end.

I've tested it on:
Chrome Version 22.0.1229.94 m
Firefox Version 10.0.1
IE Version 9.0.8112.16421
Safari Version 5.1.7
All display similar behavior on my 24" monitor. If you are testing it on Chrome or Safari, you'll need to resize the browser window to force the scroll bars to show up.

Here is a video that illustrates the behavior.

Change the position: absolute; line to position: fixed;

Thank you!