Why don't I see homeoffice and business trips on the dashboard?

If you don't see a homeoffice or business trip on the dashboard in the first widget, also make sure you don't have homeoffice and business trips set as absences. Then you would see them in the second "Who is not working today" widget. 

Another possibility as to why you don't see the top widget could be that you have the Activities module turned off. Check the visibility of the modules in the Settings / Visibility of modules section.