Anomalies when I unwrap the UV mesh After successfully producing an Unwrapped UV map on my file, I saw anomalies so I looked at the Stack Exchange listing that came up when I typed my question, and found how to remove most of them by using  W> Remove Doubles.  That still left two dots (vertices?) that I don't know how to get rid of.  Can you help?
 

Here is the same map after removing the doubles:


Also, a related question is how to get a UV image that I next created, big enough to cover the UV Map.  (Does that make sense?)
Also, as to texture size - you will need to select all and scale down to fit inside that main square that represents the image area. Add an image and choose UV Grid or Color Grid instead of Blank, and you will see the way the mesh UVs overhanging the edge 'repeat' across the image, especially if you paint on the texture.