I found a job posting on Craigslist that describes the type of applicant they want well, in technical experience and how they work as a person. However, it does not show the company name and it only glosses over what they do in their industry. How can I write a cover letter when this lack of information doesn’t help me focus or tailor the letter towards their interests wel? Should I even bother writing a cover letter to a company that doesn’t show their name or profile?
I can appreciate your dilema. And I agree that it is important to tailor a cover letter to the particular organization.
You demonstrate “due diligence” by researching the company and understanding a little bit about them.
Having said all that, my first instinct is “Do you really want to work for a company that advertises on Craigslist?!”
{From one who has applied and interviewed for countless jobs in a 30+ year career}
In my experience, I have gotten some good short term and full-time jobs from Craigslist, and I place out of a majority of the jobs in Dice and Monster. Many of the jobs posted there look for more seniority and I only have 4 years of experience. However, in those 4 years I haven’t gotten into advanced web development topics at work. You’re talking to a guy who grew up in a part of web developmentland where making a website is synonymous to Wordpress, Joomla, FTP and SEO, instead of things like test-driven Design, Agile, Doctrine, and design patterns 
So I guess I’ll pass this job for now, and look for places that aren’t hush-hush on who they are.
I think a better question to ask is, in this economy can you afford not to apply for it? You can stick your noise in the air towards craigslist all you want; however, there have been web development companies who do $10,000.00 - 20,000.00 per month in business off of it. There are companies who list on Monster, etc. who keep their company name confidential because they do not want to be flooded with crap so they use a 3rd party to evaluate the applicants.
I make quite a lot of my income form folks I’ve contacted through craigslist. There are some nut balls there, but there are also a lot of folks who are just looking to pick up someone in a hurry.
I have a general formulation for cl emails, which is a brief introduction, a list of 3-5 relevent projects, and a request for example s of the kinds of work they are producing (in the case of people hiring someone to do work for their clients) or examples of the kinds of work they are looking for (if they are and end-client in themselves).
After having sent out about 15/week for the last 18 weeks, I’ve gotten pretty good at it 
. I get about 10% responses, so it isn;t the kind of thing I like to spend a lot of thought on.
But two of my best clients at the moment have come via CL.
My last job I found on CL by accident and it turned out to be a prominent, legitimate software company. I did real well, got promoted 3 times in 3 years and made a good salary + commissions. I loved it until they sold to a larger corporation. It was a good ride for a while.
You have to use good judgement on CL, it could be a crazy place. Present yourself seriously, expect nothing, and do your research once you get a company name. I wouldn’t give up Monster or Indeed yet.