Legal issues
Talking too much about the internals of the company may get you into serious trouble. The contract you signed when you were hired may specify that under no circumstances, you won't publish anything you learnt about the way things are done in this company, things that an outsider has no way to learn otherwise.
The clause is usually done in a form of a NDA and while its purpose is to prevent the publicity about the good things, such as an innovative way of performing a given task, in court, this clause may also be used against people who are publicly explaining how bad the company is.
This alone should make you think twice before saying anything about your previous employer. If this is not enough, here are some other points to consider.
Future employers won't like you
Imagine you are looking for a job. You found a great company and you contact them. Before the interview, they search for information about you on the internet, and find your LinkedIn post which is nothing else than a rant about your previous employer.
Would it be indicative for them that you might be willing to write another LinkedIn article about them if they hire you? They probably don't want this sort of publicity, and the easiest way for them to prevent it would be to avoid contacting you.
Maybe you tried dozens of things internally to solve the problem before writing the article. A potential employer doesn't know that.
Employers do know each other
Imagine, again, that you are looking for a job and contacted a company. A person from this company looks at your CV and calls your ex-employer to ask if you're a great employee.
What would be the effect when the ex-employer will tell that you're not great, and that you spend your time badmouthing? He also has proof: your LinkedIn article.
At least don't quote the names
If you still want to publish an article, at least do it in a way which makes it difficult to associate with your ex-employer. Instead of writing:
When I worked on Microsoft Office 2013 at Redmond, [...]
write:
Once, I had to contribute to a huge project in a large company; despite the fact that the project was essential for this company, it looked like nobody cared about the [...]
It doesn't necessarily mean that the readers cannot figure out what is the company (putting your CV side by side, it may become obvious), but it requires effort, and the fact that you don't name the company in the article makes it more like “I'm telling you an interesting story” and less like “This company sucks”.
Putting it in a way that your previous employer won't find can also be beneficial. For example, if you know that your boss was reading your blog from time to time, put it somewhere else. If you know that your blog was never visited from any IP which belongs to your company, put it on your blog, rather than on your LinkedIn profile.
Practical example
I spent a year working in a company which is... not made for developers. The fact that with more than 7 years experience in C# and a profile of a developer, project manager and designer, I had to work as a code monkey all day, teamed with people who do whatever it takes to make things as bad as possible was so depressing that I just had to write about it. And so I did.
While doing it, I was aware that:
Nobody in this French company reads my blog, simply because those people don't read anything written in English.
None of the articles contains the name of the company. I'm not ranting about a specific company: instead, I just share my experience (in a form of a rant, but still). The name of the company is irrelevant: what is relevant is the problem I encountered, and eventually what I tried and what were the consequences.
A meticulous recruiter who will read my blog and search for information about me will easily find that if I doesn't agree with the way things are done within a company, I'll first try to improve those things by talking to people from this company. By searching through blog posts and other resources, there is a way to find that I actually spoke to my colleagues, to my manager, to the lead manager, to assistant director and to the CEO.
Another example: stories from my freelancing never mention the name of the customer, and are written in a way that it is impossible to find the actual name. Confidentiality here is key: saying bad things publicly about a customer would be particularly unprofessional, if not punishable by law.
