There seems to be an unspoken rule that all cartoon rigs should scale its individual parts independently. This certainly helps in animating for exaggeration. For the rigger, this feature should not be taken lightly as it causes a slew of problems. While your patience maybe forgiving, your deadline will not.
Before delving unto specific scaling issues, here are some general reminders and workflows:
Check scaling as you rig. The most common issue I encounter is when a rigger adds or checks scale at the end of the project. By that time that happens, there are already several factors that causes the scaling issue. Solving a scaling issue with one factor is relatively easy, with two is relatively hard and with three or more is certainly an event you should be concerned. This is not to say that you are at impasse, It is still possible to fix the rig but it can easily consume a day or two if you are not careful
Unchecking Inherent Transform (UIT) should be at the group level. This comes in later but whenever I mention UIT, it should be at the group level and not at the joint level, unless otherwise stated. As you might know, joint object in Maya is somewhat unique. If you scale a joint, it will only affect itself regardless if it has children.
On scaling with a double transform (or triple, if you are extremely unlucky): If you are experiencing this problem for the first time, have comfort that you are not the only one. Every rigger encounters this, specially if he is on a working spree that couldn't careless on object hierarchy. It is perfectly normal. What is not normal is you ignore this and delivered the rig.
Double transform happens when two driver objects affect a single driven object simultaneously. The keyword here is simultaneously, as it is certainly possible to have several drivers affect a single object. The fix can be simple to insanely complex but similar concept applies: separate the several drivers either on hierarchy or order of operation.
On scaling a ribbon (bendy) rig: When scaling a skinned ribbon, the ribbon geometry will scale but not the constrained joints. To scale the constrained joints, they need to be individually scale constrained to the ribbon controls (and not to the hair follicles)
On scaling a stretchy rig: Whether made through expressions or through nodes, you need to include a scale factor for the world control. Here is a general overview. There is also a comprehensive workflow where instead of using the world control. It is an interesting take but I never really had any problem on just using the first method.