When I create an ArcGISLocalTiledLayer and point it at the path to a tile package (.tpk) the MinScale and MaxScale properties are by default set to NaN.
Here's why that is a problem, if the layer is the first one added to the map the map uses the MinScale and MaxScale of the tiles in that layer to restrict zooming of the map from then on. If I then replace that tile package layer with another one with a different set of tiles at different scales the map will not zoom to them. If I could find out what the MinScale and MaxScale of the tile package was I'd be able to change the map MinScale and MaxScale when the new layer was loaded.
The values are in the tile package in the mapservice.json file but I haven't found a way to read those values using the .Net SDK.