Well, sound design is mainly creative specialist work, although it practically encompasses everything in "sound production" in general (which would make a "sound designer" more of a generalist in the audio field). Thus, to be really competent, you should know at least a bit of everything that goes into making a soundtrack (music composition, music recording, sound effects recording and creation, dialog and location recording, hiring and directing VO artists, recording VO, mixing and mastering), although it doesn't mean that you have to do everything, but rather you should know what creating a soundtrack encompasses and what kind of talent you need to hire and/or work with. Additionally, it may be beneficial to understand script writing, film making, video editing, acting, animation, game design etc. as art forms and a bit on the practical level, because those are things that affect your work as an artist, because you're interpreting the work of other artists and working towards a coherent piece of art or media with them, and knowing and being interested in what other artists do is a good way to show professionalism. You may also wish to understand the business and entrepreneurial side of things a bit, especially if you freelance or set up your own studio. Additionally, you may wish to follow your chosen medium as a consumer to have a good sense of different styles and genres that inspire you on how to do your own work and to know what others in your field/medium are doing. And well, actually consuming the medium that you work in is probably one of the most important things, because producing it is a balance between meeting viewer/consumer expectations (i.e. lending common styles, making "what they want to hear" and producing sound which supports their art experience or media consumption the best) and filling the gaps with your own personal style. A sound designer's as well as any artist's most important skill, taken that you want to be paid for doing it, is to make stuff that people want to consume, and most importantly, stuff that supports the piece that you're doing sound for in the best possible way.