As with any characteristic, too much is a problem, I suppose.
For example, when a mood changes a bit, it's no big deal. If you're working in a nuclear power plant, having unpredictable personalities wouldn't be productive, or any source of entertainment.
All traits have good aspects. eg. Some people call "attention to detail" anal, but when they're attentive to detail, they reframe in their favour. It's a matter of degree, upon reflection.
When the quality of life is affected, it's time to sit down and have a talk, or draw clear boundries about the disruption.
What a great question you posed here. I am wondering about the types of scenarios or examples of when capriciousness could be a problem. Do you mean a problem for the person who is capricious or a problem for someone in their life? (which then translates into a problem for the friendship / relationship).
Capriciousness unless I am mistaken is a personality trait from the point of view of the health care model, so whether it is a problem or not depends on the consequences of it. As Davit points out, the high blood pressure, violent mood swings etc... are negative consequences.
Unpredictability can mean that you find yourself not knowing what you will feel / do next or it can mean that you don't feel unpredictable, but people around you label you as such.
If a person feels their moods are unpredictable, there are strategies to try for this.
I am not against capriciousness 100% because I also value creativity and creative urges can come out of the blue.
I had to think on this a few days because of the definition of capricious. This would be more than just general mood swings. This I would take to be a more than normal mood swings which I believe every one has but some hide better than others. Being baited till you have a violent mood swing would not be acceptable, being either person. From a health point I think this is not healthy mentally or physically. No one needs high blood pressure or stroke. What to do about it depends I guess on whether you are giving or receiving. Myself I would not want to live in a flat lined mental state. On the other hand I would not want to be Bipolar even though medication gives the Bipolar person a pretty good life. Better than uncontrolled anxiety. This is probably the only case where avoidance is better than Medication. Again it depends on whether you are giving or receiving. Just my opinion. I chose avoidance even though it was not the complete answer.