In no particular order.
Needless to say, this is one of the most critical mistakes in any resume. If you are unable to write a spelled-check CV, then most likely you will not be able to finish any task properly, or at least that is what HR Manager's think. It is amazing how many CVs are out there with spelling mistakes, given the vast amount of free spell checkers.
Target Position Not Clear
The employer needs to know what position you are applying to from the first moment they take a look at your CV. If your target job is not clearly mentioned at the beginning of your resume, then there is a big chance that it will end up in the trash bin.
Resume lacks focus / Unrelated information
The resume should focus on the job in hand. Listing unrelated information is not going to help much. Save the space for the important stuff.
Resume items are listed in an order that doesn't consider the reader's interest
Order is important. The most relevant information should come at the top. In some cases, putting education before experience is a good decision, while not always the case. Consider very carefully what is best for you.
Abbreviations / Technical Info at the top
Most resumes will be filtered by HR Managers before they get into department heads. The HR Manager may not be familiar with industry specific words and may mistakenly throw your CV in the trash even though you may be highly qualified. Write your CV in a simple manner that can be understandable by anyone. List technical stuff a little bit down not at the top.
Hobbies / Interests details
People attempt to make their resumes a little more personal by including their hobbies and interests. Don't make it personal. Keep it professional.
Using the same CV/Resume for every job
Employers like customized CVs much more than generic ones. The "One Shoe Fits All" proved to be unsuccessful in job hunting.
Heading it with "Curriculum Vitae"
They know it is a CV, why do you have to bold it and write it in huge capital letters?
Why you left your previous employer
Keep that to the interview especially if you were fired! Including negative information like this will not help. Focus on the things that will increase your chances of getting to interview.