I am using QGIS 2.4.0 Chugiak version.
Is there an option to save selected features from a shapefile?
I couldn't find such an option in this version. I am using stand alone application.
Select the features that you are interested in in your file.
Then Right click on the layer and select "Save As".
In the save layer dialog make sure the check box "Save only selected features" is checked. See image below.