What should happen when I browse to my Windows domain name via UNC?

You ask very interesting question that may need deeper technical investigation. My opinion is that Windows "thinks" \\my.dom.com\SimpleSharedFolder is a part of some DFS namespace. But it cannot find related AD information to build a list of target servers that offer folder's contents. Explorer just displays it as empty folder.

What happens is (I suppose):

1. You open \\my.dom.com in Windows Explorer;
2. It does a simple DNS query for A DNS Records - (same as the parent) ones;
3. Most suitable DNS record is chosen from the response;
4. Windows Explorer connects to that SMB server and shows all shared folders;
5. When you open \\my.dom.com\SimpleSharedFolder DFS Namespace stuff comes into play (the redirector);
6. The target for this folder is unknown;
7. Explorer reacts with showing empty grid;

At the same time just think: "\\my.dom.com\SimpleSharedFolder" is meaningless if SimpleSharedFolder is not a part of some namespace - my.dom.com namespace for example. In your case it's not part of any namespace - only one DC has this folder shared. So it's somehow expected to see nothing accessing it via \\my.dom.com call. May be Windows Explorer should be made more robust. May be it's a bug or may be a feature :)

This is just a theory. Feel free to prove it or to consult other AD technicians.

UPDATE:

Theory proven by an experiment - I tried to access \\mydomain.lab\Dev which is simply a shared folder on a DC. Here the SMB traffic:

So DFS comes into play here via the FSCTL_DFS_GET_REFERRALS SMB call:

I think this explains everything. Hope this helps!

So I am sure you found the SYSVOL folder (where Group Policy files are stored) at \\my.dom.com. By default that is replicated between all DC's in the domain ('08 uses via DFSR [Distributed File System Replication] & '03 uses FSR [File Replication Service]) so clients can query the domain \\my.dom.com & whichever DC is closet responds

I speculate \\my.dom.com is actually handled (resolved) differently then \\1.1.1.1 & it has something to do with SMB vs DFS/N. I can't give you a direct answer to all of your questions, but I do believe that is a start. Here is another article with some more info