One small thing that I haven't seen yet (in FF or Chrome) is a feature where I could get the IP address that was used to retrieve a given resource in the network tab. This would be hugely helpful when dealing with sites that are backed by more than one server. Also, ability to reset DNS cache (BTW, DNS cache seems to be shared between private and regular browsing modes).
<edit>The ability to lock onto a specific IP for a given domain would be pretty kick-ass too. Not a replacement for /etc/hosts, but just choosing one of the 2 IP's for example.com, etc.</edit>
Another nice feature would be to get the network tab to ignore resources loaded from external domains, only show external resources, or show both. Maybe even more fine grained with/without subdomains.