I'm experiencing a similar problem. I've looked through the reference, but I don't see anything that lets you place overlapping labels. When I noticing is that no matter how far I zoom in, I have at least one label that never does draw. These are my county boundaries, which I use all the time, so I can't imagine there is anything wrong the layer itself. This county is shaped a little differently, sort of an upside down L. I wonder if the labeling for polygons is based on extent. In this case the center of that extent doesn't fall within the polygon itself. The county name is Iron, so it's not like its a long name!
It seems like a bug to me. I'm using version 3.10 of the API.
There's something going on with the algorithm. I'm getting the same thing. A very simple case below shows a label layer applied to a half-township section grid. I am also at 3.10 and still get missing labels, regardless of various parameter changes I've applied
I think it might be specific to version 3.10. I have some slightly older code at version 3.9, and it draws fine. If I switch my 3.10 references to 3.9, it works. I take that back. In the 3.9 version, it wanted the field name as ${fieldname}. In 3.10, it only worked if without the $. Obviously there's been some changes made between the version. Let's hope ESRI staff read these threads for this sort of thing.
Tracy,
You can always call attention to a person (like one of the Javascript API experts) in a post by using @ then typing their name. Like this Tracy Schloss. This will put an alert into their mailbox.