<p>I have a ASP.Net website that is failing on AJAX postbacks (both with ASP.Net AJAX and a 3rd part control) in IE.    FireFox works fine.  If I install the website on another machine without .Net 3.5 SP1, it works as expected.</p>

<p>When it fails, Fiddler shows that I'm getting a 405 "Method Not Allowed".  The form seems to be posting to pages other than page I'm viewing.</p>

<p>The form's action is "#" for the page on the broken website (with SP1).  The form's action is "Default.aspx" for the same page on a website without SP1.</p>

<p>Any ideas?</p>

These are my observations rather than a full answer:
My guess (without trying to re-produce it myself) is that a couple of things may be happening as the DataSet tries to 'flatten' a hierarchical structure to a relational data structure.
1) thinking about the data from a relational database perspective; there is no obvious primary key field for identifying each of the Foo elements in the collection so the DataSet has automatically used the ordinal position in the file as an auto-generated field called Foo-Id.
2) There are actually two elements called 'Foo' so that probably explains the generation of a strange name for the column 'Foo-Id-0' (it has auto-generated a unique name for the column - I guess you could think of this as a fault-tolerant behaviour in the DataSet).