The Crop tool in Adobe Acrobat is non-destructive; this means, once you've made a selection and you're then shown your cropped area, the PDF will still retain all the other canvas data and elements. This can cause issues later on, so if you're after a true crop of an area within your PDF, this is how to do it...
Make your crop, as usual, using the Crop tool.
Now this is the part that makes all the difference: export the cropped PDF as a Postscript file.
Close Acrobat. Double-click and open the Postscript file. A window will appear, which processes the PS file and generates a new PDF file. This new PDF file is now a true crop.
Thanks to those in the following discussion: