The audio player, and videos will create apparent errors when you do a validation report, but they are not something we can do anything about. The other thing to remember is that the effects of one blogger introduced error can actually cascade down through the markup and create apparent errors in other parts of the page. I've worked on blogs where they had 50 errors being reported and after I fixed 5 things, all the errors had gone away.
The code for the blog explosion is definitely broken. One thing is that it has border 0pt, and that is wrong, it should be border 0 . There is no need to put a unit when the value is 0. There are also a number of syntax errors and you had no closing "p" tags for the 4 different sections of code. Replace the code you have in that text widget with the following and it should straighten out a bunch of errors.
<p style="text-align: center;"><a id="clustrMapsLink" href="http://www2.clustrmaps.com/counter/maps.php?url=http://iwanticewater.wordpress.com/"><img style="border: 0;" title="Locations of Visitors to this Blog" src="http://www2.clustrmaps.com/counter/index2.php?url=http://iwanticewater.wordpress.com/" alt="Locations of Visitors to this Blog" />
</a></p>
<p style="text-align: center;"><a href="http://www.blogexplosion.com/index.php?ref=IzaakMak"><img src="http://banners.blogexplosion.com/button1.gif" border="0" alt="" width="88" height="32" /></a></p>
<p style="text-align: center;"><a title="Philosophy Blogs - Blog Catalog Blog Directory" href="http://www.blogcatalog.com/directory/philosophy"><img style="border: 0;" src="http://assets.blogcatalog.com/buttons/blogcatalog4.gif" alt="Philosophy Blogs - Blog Catalog Blog Directory" /></a></p>
<p style="text-align: center;"><a title="counter for wordpress" href="http://www.statcounter.com/wordpress.org/" target="_blank"><img src="http://c.statcounter.com/4857659/0/aa2dc22e/0/" border="0" alt="counter for wordpress" /></a></p>