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1.  Never actually launching it:  This is likely the most common mistake.  Sure, you've been meaning to get your blog kicked off.  You may have even authored your first article.  But guess what, it's not a blog until you actually publish something.
2.  Using a sub-domain (ex:  If you're going to go to the trouble to start a blog, then you owe it to yourself to get started right.  Even if you decide to use one of the many popular free blogging services, you should register your own domain name.  There are many reasons for this, but the most important is control over your website URL.  This is one of the few decisions about your blog that is going to be difficult to fix later.  Trust me on this one, the price is worth it.  [Note to self:  Add a check to the website grader to let people know when they've made this blunder]
3.  Spending too much time on design: Don't let the design of your blog get you bogged down.  Pick one of the many existing templates out there that are free or close to it and go ahead and get started.  You can always change templates later.  Besides, blogs are fundamentally about content.  Aesthetics help, but your first focus should be on authoring great content.
4.  Not telling anyone about it: The beginning days of a blog are the hardest.  You don't have anyone linking to you, the search engines are not ranking you (and maybe not even indexing you).  So, there's really only one source of traffic:  Direct contact.  The best way to get a new blog launched is to tell people in your network that you now have a blog.  Many people are a little reluctant to do this becomes it seems vain or boastful.  As long as you're sending the notification to people that have an interest in your topic, there's nothing wrong with it. 
5.  Getting discouraged too early: Most things in life worth doing take time.  Blogging is no different.  You should give yourself at least 6 months (perhaps even a year) to determine what kind of interest there is out there before giving up due to lack of traffic.  Early momentum is hard, but once things start moving, lots of things will start working in your favor.
6.  Too many blidgets: Given how easy it is to add various blog widgets to your blog, it's tempting to go overboard.  Resist the temptation.  In the early weeks, focus on the basics:  Content, comments, categories and perhaps a blog roll.  Save the fancy stuff for later.
7.  Monetizing too early: Just because Google makes it easy to throw ads up on your blog doesn't mean you should.  With minimal traffic, the amount of money you are going to make is neglible (probably pennies a day).  If you're serious about blogging, you'll first focus on building an audience before even attempting to try and make money at it.  Trying ads out on your blog too early will reduce the chances of your getting that critical early traffic.
I'm sure there are many more common mistakes.  Which ones do you see people make the most often?  Share your thoughts and leave a comment and make the blogosphere a better place.