Hi Derek,
thanks for your reply. The problem persists in different Web Browsers (Firefox, IE, Chrome) and also after clearing the cache.
Actually a colleague of mine discovered it and I reproduced it. I also tried as a different portal user (administrator), same behaviour.
The portal is installed on an internal server, so I cannot send you the link.
Now I created a new map, just adding
Map Contents
Soil_Survey_Map: http://services.arcgisonline.com/arcgis/rest/services/Specialty/Soil_Survey_Map/MapServer
Topographic: http://services.arcgisonline.com/ArcGIS/rest/services/World_Topo_Map/MapServer
and from this I just create a Web application (Share --> Make a Web Application --> Web AppBuilder)
I can see this behaviour directly on the Web AppBuilder page leaving everything to the default, pressing first the Legend button and then the Layer List (pressing the other way round everything works).
It seems that something is initialised wrongly.
I am using the Web AppBuilder for the Portal, not the developer edition.