When you apply for a job it's tempting to do anything you can to stand out. Sometimes that's a good idea. If, for example, you're a long-shot candidate, it might make sense to make a joke, try something bold, or make a big statement through your cover letter to get the recruiter's attention.
There are limits to how helpful that can be, and there's absolutely bad attention. Your goal in applying is to get an interview. It's not to have the recruiter talk to other people about your candidacy without even considering calling you in for an interview.
These are common mistakes that happen during the interview process (not just on cover letters). If you avoid them you'll have a much better chance of getting hired.
1. Don't insult the company
It's fine to tell the company all the positive things you bring to the table. You can even talk about your history of improving processes, increasing sales, or otherwise making the companies you work at better.
You should never point out what you think the company is doing wrong. That's presumptuous and a tad obnoxious. It's also possible that you don't have the full picture and by being bold you'll just look silly.
2. Don't respond slowly
Sometimes a recruiter will see your cover letter and resume and have an immediate question. When that happens, the recruiter may shoot off a quick email designed to answer that question so he or she can decide whether or not to offer you an interview.
If you don't answer quickly, you may miss your opportunity. This is a case where "quickly" means within a few hours, because if you take longer, the recruiter may still like you but have already set up interviews with other candidates.
3. Don't talk about the job you really want
Your cover letter offers an opportunity to sell yourself as a candidate for this job. It's not a chance to tell the recruiter or hiring manager about all of your hopes and dreams for the future. Focus on the opportunity that's in front of you and why you're a good fit.
It's great if you someday want to be a poet, a philosopher, a CEO, or whatever else, but that's generally not relevant during the hiring process. Even if asked about your long-term goals, try to keep your answer relevant to the job/profession at hand.
Gauge your risk
If you have very little chance of getting an interview, it might be worth going out on a limb. You can use your cover letter to make a case for interviewing using metrics that aren't clearly what the hiring manager has laid out in the job ad.
For example, I once claimed my experience running a retail business and a factory qualified me to edit a business news publication. That didn't quite work -- though I did get a response from the person doing the hiring, and later (once I had some actual business journalism experience) I got an interview.
It's a smart idea to highlight things about yourself that qualify you for the job which may not be apparent just from your resume. Don't, however, veer into "I'd be a great physician because I've seen every episode of ER," because while you might get a laugh, you're wasting everyone's time.