I have a legend created in ArcMap 10.1 which appears to be generating an abnormal white gap to the right of the legend content.
How can I remove this?
On the third screen of the legend wizard you have the option to assign the gap that you want between the frame and the object in the legend (this also applied to neatlines). Adjust that until it looks right.
I too also convert features to graphics, but this is the very last thing I do on a map; it is no longer tied to the map features and if you change something it has to be done all over again.
I would recommend converting your legend to graphics. This will allow you to make edits to all elements - I find it especially useful when encountering artifacts in raster legends. Note - make sure your map is finalized before converting because it will no longer dynamically update with label/color changes.
Once you have converted your legend to graphics you can Ungroup the elements by right-clicking and make edits to each part individually using the Graphics toolbar.