I could be totally wrong but here it goes...
My boss (who is on the admissions committee at University of Awesomenes) told me it is always important in your first paragraph to state your purpose. Why are you applying to graduate school? What is your purpose? A lot of people do not state that and it drives adcoms crazy. Your first paragraph can be a brief introduction about how you got interested in your field, some experience you have in it, and lastly, what motivated you to seek a PhD? Was it the experience you had as a research assistance was so great? Was it the little career advancement you saw in filed X as a basic researcher? Whatever it is that motivated you state it, whether it is at the end of the paragraph or the beginning, adcoms want to know why are you applying, and why should they invest $25,000 in you for the next 5+ years and are you worth it? If so, prove it, show them.
Also, it may seem really silly but if you have a writing center on campus, use it. They have people who specialize in technical writing, scientific writing, admission to graduate school writing, grant writing, etc. Also, the writing center is free. I went there 3 times and at my school, you were able to email them your drafts if you could not meet with them.
Something interesting, I was told was to not write a lot of crap about every research position you ever held in the past. It is great you were involved in lab Totally Rad for 1 year and lab Kinda-not-so-awesome for 3 years, but you don't need to list every thing you did, they can look at your CV to see all the positions you held. Highlight the most important ones that speak to your potential future as a graduate student in their program.
Lastly, it is important to state your long term career goal(s). This can be vague such as "a career in academia" or whatever. Not everyone knows exactly what they want to do, and not everyone wants to be Principal Investigator (PI) and that is fine. Point is, they want to know you can complete their program and go out and get a job and represent their program well.
This is all advice I received from students and faculty members on adcoms. It is not applicable for every school or program but just a overarching outline of what to address in your SOP.
I hope that helps and does not come off abrasive.