You don't need to correct the codes of Adsense if you add the codes onto the side-bar on your blog since the side-bar is using HTML/Javascript which is not allow xml.

But if you go to Dashboard > Design > Edit HTML (This HTML editor allows xml), you need to modify the codes of Adsense :
1) Change & into &
2) Change < into &lt;
3) Change > into &gt;
4) Change " into &quot;
5) Change ' into &apos;
For example, the blue codes below is original codes of Adsense, and the yellow codes below is what I have after changed all the symbols :
<script type="text/javascript"><!--
google_ad_client = "pub-0690220431785051";
/* 728x90, created 8/7/10 */
google_ad_slot = "8652075993";
google_ad_width = 728;
google_ad_height = 90;
//-->
</script>
<script type="text/javascript"
src="http://pagead2.googlesyndication.com/pagead/show_ads.js">
</script>

&lt;script type="text/javascript"&gt;&lt;!--
google_ad_client = &quot;pub-0690220431785051";
/* 728x90, created 8/7/10 */
google_ad_slot = &quot;8652075993&quot;;
google_ad_width = 728;
google_ad_height = 90;
//--&gt;
&lt;/script&gt;
&lt;script type=&quot;text/javascript&quot;
src=&quot;http://pagead2.googlesyndication.com/pagead/show_ads.js&quot;&gt;
&lt;/script&gt;

Please double check to make sure you have changed all the symbols on the codes already, if you are lazy to change the codes by yourself, you can always use the tool on this page to help you change the code : http://blogcrowds.com/resources/parse_html.php.

You might also like this : http://ye5.blogspot.com/2010/12/how-to-use-google-adsense.html