OGR Layer Intersection

There are some errors in your script but it is not the most important problem:

You cannot create a valid shapefile without specifying the geometry of the layer:

driver = ogr.GetDriverByName('ESRI Shapefile')
dstshp = driver.CreateDataSource('SomeFilename.shp')
dstlayer = dstshp.CreateLayer('mylayer',geom_type=ogr.wkbPolygon)

And you don't know a priori (upfront) the geometry of the resulting intersection layer. The intersection of two polygon layers is different from the intersection of a polygon layer and a polyline layer for example.

For that, you can get the geometry of the intersection by:

For example (with two polygons shapefiles):

layer1.GetGeomType()
3 # -> polygon
# create an empty geometry of the same type
union1=ogr.Geometry(3)
# union all the geometrical features of layer 1
for feat in layer1:
    geom =feat.GetGeometryRef()
    union1 = union1.Union(geom)
# same for layer2
union2=ogr.Geometry(layer2.GetGeomType())
for feat in layer2:
    geom =feat.GetGeometryRef()  
    union2 = union2.Union(geom)
# intersection
intersection = union1.Intersection(union2)
print intersection.GetGeometryName()
'MultiPolygon'

At this stage, you can save the resulting geometry to a shapefile (without the fields of the original layers):

dstshp = driver.CreateDataSource('SomeotherFilename.shp')
dstlayer = dstshp.CreateLayer('mylayer',geom_type=ogr.wkbMultiPolygon)

But if you want to use your script (a MultiPolygon is a collection of Polygons):

driver = ogr.GetDriverByName('ESRI Shapefile')
dstshp = driver.CreateDataSource('SomeFilename.shp')
dstlayer = dstshp.CreateLayer('mylayer',geom_type=ogr.wkbPolygon)
for feature1 in layer1:
   geom1 = feature1.GetGeometryRef()
   attribute1 = feature1.GetField('FieldName1')
    for feature2 in layer2:
       geom2 = feature2.GetGeometryRef()
       attribute2 = feature2.GetField('FieldName2') 
       # select only the intersections
       if geom2.Intersects(geom1): 
          intersection = geom2.Intersection(geom1)
          dstfeature = ogr.Feature(dstlayer.GetLayerDefn())
          dstfeature.SetGeometry(intersection)
          dstfeature.setField(attribute1)
          dstfeature.setField(attribute2)
          dstfeature.Destroy() 

Don't forget to define the fields before (look at Python GDAL/OGR Cookbook:Vector Layers). And it is much easier with the module Fiona

I thought I'd add my experience here. I've been working with situations where I might need to merge hundreds or thousands of polygons and the Union solution didn't quite cut it - the time to get the intersection of 1 polygon in 1 layer against a couple of hundred polygons in 1 other layer took ~15 secs. I managed to cut it down to 0.08ms by adding each polygon to a MultiPolygon and avoiding doing a Union for every polygon and Simplifying the entire geometry at the end of the loop:

    union = ogr.Geometry(ogr.wkbMultiPolygon)
    for feat in 
        union.AddGeometry(feat.GetGeometryRef())
    union1.Simplify(0)

Actually, I found for my purposes I didn't even need the Simplify - the intersection geometry seemed to behave as I needed it to without the extra function call.