For those with UG science degrees, when it is said, "you probably will need a higher degree," it goes without saying that they will also need to be able to write well (and like it). Writing is an essential part of the job, but if that was it, it would be very much like other forms of legal writing. Except it isn't like other forms of legal writing, because it requires a fairly broad sampling of technical knowledge to have any idea about what is being written. You can emphasize your writing skills, but keep in mind they will focus more on what sort of technical work you have done, and take it for granted you can write well.
Specializations generally refer to general technical areas, such as bio/chem, electrical, and mechanical. Those are essentially the main ones, and certain degrees tend to be pushed towards one of these areas (or they don't fall under any of them and are undesirable). Physics is pushed into the electrical and mechanical piles. Sometimes, a particular firm will get a LOT of a particular type of technology (e.g. analog circuits), and would prefer someone with a good amount of experience with it, but this isn't the case the majority of the time, because the firm will likely need the person to do other types of applications, and so place more weight on general technical ability. Sometimes companies will want someone with a very particular background, but nearly all in-house positions are not entry level positions, and generally instead of being requirements, the particularized list of background experience is closer to a wish list.
California is a big market, about on par with DC, but it is hard to stay in one very particular area unless almost any firm would want you (e.g. you have a lot of the experience they most want already).