I am not sure, if this is bug (unwanted feature), or wanted feature, but assuming the latter: this is tested to be present in frontend 6.0.3 (and also 5.4.12):

Steps to reproduce:

1. Create map with elemtent of host group type.
2. Link it with host group containing hierarchical sub-groups containing hosts with problems.
3. Save and display map.

Result:

Element indicating "OK" status of Problems. When clicked on "Problems" in element context menu, problems in sub-hostgroups are displayed.

When host group in element re-linked to specific host group containing problems directly (not indirectly via sub-group), then map will indicate them.

Expected:

As I see it, consistent/logical approach is to indicate the same problems, that displayed when navigating to "Problems" via host group map element context menu.