Surely there must be some cons to using adjustment layers. Actually, there are a couple:
Adjustment layers do not travel across color-mode conversions. For example, changing from RGB to CMYK requires you either to discard your adjustment layers or burn them onto a flattened version of the file. In such situations, it's a good idea to save an RGB copy of the file before converting to CMYK; that way you retain your adjustment layers and have the option of returning to your file should you need to.
Some features, such as Shadow/Highlight, aren't available as adjustment layers. Of course, you can duplicate the Background layer (Command/Ctrl-J), and then apply your Shadow/Highlight adjustment to the copied layer. Although you can't double-click to edit the adjustment, you can lower the opacity of the duplicated layer to lessen the effect, or change its blend mode for a different result.