I am early into the configuration of an ASA 5510 on version 8.3(2) of the OS and 6.3(4) of ASDM.
One oddity I've noticed already is that when I've created Network or Service Groups in ASDM, some of them appear immediately in ASDM and some never do. Here are two examples of groups that I can see in the text configuration but not in ASDM:
The names are similar, so I've wondered if there is something about the names that are causing ASDM to not see them, but the help text for the group name field says to: "Use characters a to z, A to Z, 0 to 9, a period, a comma, a dash, or an underscore. The name must contain 64 characters or fewer." My names certainly fall within the scope of what should be considered a legal name. I created additional groups for testing, with the same object members and they show up fine, e.g.
The DM_INLINE objects are custom objects that are automatically created and edited when using things like the Access Rules pane. Because these are automatically managed by ASDM, there is no place to view/edit them (though they will be automatically updated when the rule that references them is changed).
If you want to have direct control over the objects, you'll need to create them with a name other than DM_INLINE_x. These should show up in the Objects pane and you'll be able to edit and re-use them throughout the config. Otherwise, ASDM will transparently manage the DM_INLINE objects.