Fastest way to add new node to end of an xml?

You need to use the XML inclusion technique.

Your error.xml (doesn’t change, just a stub. Used by XML parsers to read):

<?xml version="1.0"?>
<!DOCTYPE logfile [
<!ENTITY logrows    
 SYSTEM "errorrows.txt">
]>
<Errors>
&logrows;
</Errors>

Your errorrows.txt file (changes, the xml parser doesn’t understand it):

<Error>....</Error>
<Error>....</Error>
<Error>....</Error>

Then, to add an entry to errorrows.txt:

using (StreamWriter sw = File.AppendText("logerrors.txt"))
{
    XmlTextWriter xtw = new XmlTextWriter(sw);

    xtw.WriteStartElement("Error");
    // ... write error messge here
    xtw.Close();
}

Or you can even use .NET 3.5 XElement, and append the text to the StreamWriter:

using (StreamWriter sw = File.AppendText("logerrors.txt"))
{
    XElement element = new XElement("Error");
    // ... write error messge here
    sw.WriteLine(element.ToString());
}

See also Microsoft’s article Efficient Techniques for Modifying Large XML Files