Does the shapefile support mixed geometry types (ie. point and polygon all in the same file)?
Answer can be found from the official specification http://www.esri.com/library/whitepapers/pdfs/shapefile.pdf.
All the non-Null shapes in a shapefile are required to be of the same shape type. The values for shape type are as follows: Value Shape Type 0 Null Shape 1 Point 3 PolyLine 5 Polygon 8 MultiPoint 11 PointZ 13 PolyLineZ 15 PolygonZ 18 MultiPointZ 21 PointM 23 PolyLineM 25 PolygonM 28 MultiPointM 31 MultiPatch Shape types not specified above (2, 4, 6, etc., and up to 33) are reserved for future use. Currently, shapefiles are restricted to contain the same type of shape as specified above. In the future, shapefiles may be allowed to contain more than one shape type. If mixed shape types are implemented, the shape type field in the header will flag the file as such.
Notice also that points and multipoints can't be saved into same shapefile while lines and polylines can, as well as polygons and multipolygons.
A shapefile does not support mixed geometry. A shapefile either consists of points, polylines or polygons, but not more than one.
See this article for more: Shapefiles