Mixing forward and inverse kinematics So I've made a simple, yet effective human rig with both arms and legs configured to use inverse kinematics (with an IK constraint, pole and target all set up). 

This works fine for me and does the job, however, I prefer most of the time to mix forward kinematics and inverse kinematics to set up a pose. Is there a way I can be able to use my IK constraints for the rig's arms and then tweak it up a little rotating the actual arm's bones?
There is no built-in way to perform that task.

Many rigs provide python scripts that show panels in the 3dview for controls such as layer display and IK/FK switching, many also include scripts that snap IK bones to the position of FK bones and vice versa.

You can find the rigify scripts that are included with blender within the addons folder where you can look at how this can be achieved.

Most animators will tend to use one or the other depending on the actions being animated, keying the IK/FK influences on a transition frame when they change over. I believe you will find it difficult to be using both on every frame and only create extra work for yourself.