What are the main advantages of paying for DNS hosting like Zerigo or SlickDNS instead of using the one provided for free with web host companies (E.g. Linode's DNS Manager)?
I'd say the main reason to use a DNS hosting service is to consolidate your DNS management for all of your domains regardless of registrars or server hosting providers. E.g., I personally have domains registered with 5 registrars and use two server providers. And because they specialize in DNS, DNS hosting providers should have superior interfaces, APIs and support for DNS hosting compared to generalist hosting providers.
The SlickDNS interface has two features in particular that I haven't seen in any other DNS hosting service: automatic management of "alias domains" and mapping IP addresses to named servers. See https://www.slickdns.com/features/ for details.