Does Django scale?
I don't think the issue is really about Django scaling. 
I really suggest you look into your architecture that's what will help you with your scaling needs.If you get that wrong there is no point on how well Django performs. Performance != Scale. You can have a system that has amazing performance but does not scale and vice versa.
Is your application database bound? If it is then your scale issues lay there as well. How are you planning on interacting with the database from Django? What happens when you database cannot process requests as fast as Django accepts them? What happens when your data outgrows one physical machine. You need to account for how you plan on dealing with those circumstances.
Moreover, What happens when your traffic outgrows one app server? how you handle sessions in this case can be tricky, more often than not you would probably require a shared nothing architecture. Again that depends on your application.
In short languages is not what determines scale, a language is responsible for performance(again depending on your applications, different languages perform differently). It is your design and architecture that makes scaling a reality. 
I hope it helps, would be glad to help further if you have questions.
I'm building a web application with Django. The reasons I chose Django were:

I wanted to work with free/open-source tools.
I like Python and feel it's a long-term language, whereas regarding Ruby I wasn't sure, and PHP seemed like a huge hassle to learn.
I'm building a prototype for an idea and wasn't thinking too much about the future. Development speed was the main factor, and I already knew Python.
I knew the migration to Google App Engine would be easier should I choose to do so in the future.
I heard Django was "nice".

Now that I'm getting closer to thinking about publishing my work, I start being concerned about scale. The only information I found about the scaling capabilities of Django is provided by the Django team (I'm not saying anything to disregard them, but this is clearly not objective information...).
My questions:

What's the "largest" site that's built on Django today? (I measure size mostly by user traffic)
Can Django deal with 100,000 users daily, each visiting the site for a couple of hours?
Could a site like Stack Overflow run on Django?