Well, I will share some ideas with you regarding this subject.
Speeding up stuff
If you implement the BlogTOC widget in the standard way, the entire code of the widget is placed in a Blogger Page Element, usually somewhere at the top of you blog.
Now, while your Blog is loading, all code is processed from top to bottom. The piece of code that is the most time-consuming is the code that retrieves the Blogger Feed, parses it, and puts the data in a set of javascript arrays. This slows down loading, but once the data has loaded displaying it is done lightning-fast.
A good solution is, to move the retrieval-code to a page element that is completely at the bottom of your blog page.
I have moved the code to the bottom of the footer, and that has sped up loading a lot.
The code you have to move is this:
<script src="http://yourblog.blogspot.com/feeds/posts/default?alt=json-in-script&start-index=1&max-results=100&callback=loadtoc"></script>
Automatic display of TOC
If you want the TOC to auto-display, add a simple line of javascript code at the end:
<script type="text/javascript">showToc();</script>
