Is there any sort of downside for a URL being changeable?

Depends. Let's look at your question's URL. Right now the URL is:

webmasters.stackexchange.com/questions/3079/should-i-use-a-file-extension-or-not

As you noted, if you change the question's title the URL will change, too, and become:

webmasters.stackexchange.com/questions/3079/file-extensions-are-yummy

Now, if Google has the original URL indexed and that original URL is no longer valid, then we have a problem, both at the SEO level and, more fundamentally, anyone who's linked to the question or bookmarked the question will not have a broken link and get a 404.

However, this is not how it works on StackExchange. It seems that StackExchange looks at the question ID and ignores the title part afterward. As you noted, you can visit http://webmasters.stackexchange.com/questions/5376 and it loads your question. You can also visit http://webmasters.stackexchange.com/questions/5376/file-extensions-are-yummy (or http://webmasters.stackexchange.com/questions/5376/whatever-dude) and it works, too!

So if you change your question's title and the "new" URL is

webmasters.stackexchange.com/questions/3079/file-extensions-are-yummy

That doesn't mean your old URL won't work - it still will. As well as the new one.

At this point you may be rightfully concerned that there are duplicate URLs. If there are a number of links to your original URL (webmasters.stackexchange.com/questions/3079/should-i-use-a-file-extension-or-not) and a number to the new one (webmasters.stackexchange.com/questions/3079/file-extensions-are-yummy) you are going to be splitting the page ranking in Google and other search engines. Fortunately, this can be mitigated using the <link rel="canonical" /> tag.

Google provides a good description of <link rel="canonical" /> in their blog entry Specify your canonical. In short, you can use this tag to say to the search engine, "I don't care about the URL you used to reach this page, please treat it as if you were visiting via this other URL."

On StackExchange, the canonical URL is the URL of the original question title (or so I presume). If you do a view/source on this page you'll see the following tag:

<link rel="canonical" href="http://webmasters.stackexchange.com/questions/5376/seo-and-changeable-urls">

Likewise, if you visit http://webmasters.stackexchange.com/questions/5376 or http://webmasters.stackexchange.com/questions/5376/file-extensions-are-yummy or http://webmasters.stackexchange.com/questions/5376/whatever-dude the canonical <link> tag stays the same. I presume its value is fixed, regardless of whether you actually change your question's title.

So, long story short, if you have things setup correctly then there is no downside for a URL being changeable. But if you generate 404s or do not use the canonical tag (or some other form or URL rewriting) then there are downsides.

Happy Programming!

Is there any sort of downside for a URL being changeable?

Depends. Let's look at your question's URL. Right now the URL is:

webmasters.stackexchange.com/questions/5376/seo-and-changeable-urls

As you noted, if you change the question's title the URL will change, too, and become:

webmasters.stackexchange.com/questions/5376/file-extensions-are-yummy

Now, if Google has the original URL indexed and that original URL is no longer valid, then we have a problem, both at the SEO level and, more fundamentally, anyone who's linked to the question or bookmarked the question will not have a broken link and get a 404.

However, this is not how it works on StackExchange. It seems that StackExchange looks at the question ID and ignores the title part afterward. As you noted, you can visit http://webmasters.stackexchange.com/questions/5376 and it loads your question. You can also visit http://webmasters.stackexchange.com/questions/5376/file-extensions-are-yummy (or http://webmasters.stackexchange.com/questions/5376/whatever-dude) and it works, too!

So if you change your question's title and the "new" URL is

webmasters.stackexchange.com/questions/3079/file-extensions-are-yummy

That doesn't mean your old URL won't work - it still will. As well as the new one.

At this point you may be rightfully concerned that there are duplicate URLs. If there are a number of links to your original URL (webmasters.stackexchange.com/questions/5376/seo-and-changeable-urls) and a number to the new one (webmasters.stackexchange.com/questions/5376/file-extensions-are-yummy) you are going to be splitting the page ranking in Google and other search engines. Fortunately, this can be mitigated using the <link rel="canonical" /> tag.

Google provides a good description of <link rel="canonical" /> in their blog entry Specify your canonical. In short, you can use this tag to say to the search engine, "I don't care about the URL you used to reach this page, please treat it as if you were visiting via this other URL."

On StackExchange, the canonical URL is the URL of the original question title (or so I presume). If you do a view/source on this page you'll see the following tag:

<link rel="canonical" href="http://webmasters.stackexchange.com/questions/5376/seo-and-changeable-urls">

Likewise, if you visit http://webmasters.stackexchange.com/questions/5376 or http://webmasters.stackexchange.com/questions/5376/file-extensions-are-yummy or http://webmasters.stackexchange.com/questions/5376/whatever-dude the canonical <link> tag stays the same. I presume its value is fixed, regardless of whether you actually change your question's title.

So, long story short, if you have things setup correctly then there is no downside for a URL being changeable. But if you generate 404s or do not use the canonical tag (or some other form or URL rewriting) then there are downsides.

Happy Programming!