Does Django scale?
Even-though there have been a lot of great answers here, I just feel like pointing out, that nobody have put emphasis on..
It depends on the application 
If you application is light on writes, as in you are reading a lot more data from the DB than you are writing. Then scaling django should be fairly trivial, heck, it comes with some fairly decent output/view caching straight out of the box. Make use of that, and say, redis as a cache provider, put a load balancer in front of it, spin up n-instances and you should be able to deal with a VERY large amount of traffic.
Now, if you have to do thousands of complex writes a second? Different story. Is Django going to be a bad choice? Well, not necessarily, depends on how you architect your solution really, and also, what your requirements are.
Just my two cents :-)
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?