A Google Custom Domain is an elegant and simple way to have a Blogger blog published to a non BlogSpot URL - if you get the DNS addresses setup properly.
Setting up the addresses was very simple, using the "Buy A Domain" wizard. Some bloggers spurn the wizard, and roll their own - and that is where many custom domain problems start.
If you use "Buy A Domain" in setting up your custom domain, you'll get a domain with DNS hosted by eNom or GoDaddy. We are somewhat familiar with the DNS wizards provided by both registrars. The DNS wizard (assuming that one exists) provided by a third party registrar (ie not either eNom or GoDaddy) may or may not have similar options.
Two well known and very significant variations in the policies and procedures used by any registrar are absolute vs relative addresses, and how the domain root is denoted, in a referral record. Besides these differences, you'll need to know how to use the wizard itself. The eNom and GoDaddy wizards, for instance, are very different from each other.
Besides the details of using the wizards, the allowable wizard settings will vary. Each registrar tunes its DNS servers, and each will have their own idea of how long a DNS record should exist, in cache, on your local DNS server. The "TTL" ("Time To Live") setting has implications that affect every custom domain.
Some registrars, too, just can't support the settings required for a reliable custom domain.
If you must use a third party registrar (ie not eNom or GoDaddy) for your DNS hosting, please pick your registrar carefully and discriminately.