What analytics tool are you using? I know that both Google Analytics and SiteCatalyst have functions where you can make a note of changes - make sure you've recorded the date of the change so you can compare back and forth and as time goes on, remember exactly when the switch happened.

I would also run some comparison reports for equal amounts of time before and after the switch - things like your most popular pages by organic traffic, home page visits, etc. That will show you right away if an important page has stopped doing well.

In the Moz tool, tracking rankings before and after is definitely a good thing to do. You should also dig in and see which pages are ranking for your target terms before and after the switch to make sure it's still the page you want ranking for the keyword you want.

Lastly, don't forget that your site switch didn't occur in a vacuum. Take into account factors such as seasonality that could also be impacting your traffic post-switch.

I agree with Sean - I've never heard of an official limit to image filenames in terms of length alone. Since the file name is almost always part of the image URL, you could be running the risk of too-long URLs but that's a relatively minor problem. I would make extra sure that your file names don't appear keyword-stuffed, though - so watch out for things like repeating keywords or having all variations of a keyword. There's a big difference between widgets-extralarge-round-blue-widgetmaker.jpg and blue-widgets-best-blue-widgets-blue-widgets-online-free-shipping, if that makes sense. Other than that you should be fine.

DA doesn't usually transfer very well across subdomains - so it's likely the DA from www.example.com is already not affecting subdomain.example.com.

It's certainly possible to keep the subdomain alive, but I'd be a little concerned about what it would do for your brand. If you're sending the message that example.com is now newexample.com, but then keeping things running at example.com, it could create a lot of consumer confusion. From a DA stance you should be OK, though, especially if you take some extra time to promote the subdomain and the new site after launch.

You may still not see pages from the new domain and the old subdomain ranking in the same SERPs, though - Google is often pretty good at figuring out when multiple sites are owned by the same people.

The basic idea behind hub linking is that there are certain websites that are "hubs" for information - that is, they are one place that you can go to get resources on a topic.  A lot of times these domains link out a lot, because they want to showcase other websites that have good information resources on the topic.  They often do have good page authority, if they are good resources on the topic, because people link back to them.

One thing to look out for when engaging someone to do Hub linking is, you want to make sure the sites you're getting links from are actually relevant resources that real people are using.  A lot of "hub" pages are created solely for SEO purposes and tend to have thin content and too many links, which can be a sign to Google that the link is a shady one.  So it's important to be judicious in selecting a hub page to target for links, and I would advise against trying to create one yourself unless you have a long-term strategy for how to continue adding content and making it useful.