1) Vector: Your logo needs to be scalable so you should design it using vector based programs (Adobe illustrator, Corel Draw) or some other vector software.
2) Unoriginal logo design: Your logo should be original to the task at hand. The logo and branding strategy go hand in hand so be sure to create something unique and memorable.
3) Too complicated: Many designers try to complicate their logos by adding lots of details, too many words, taglines, etc. Keep it simple! Your logo will be more memorable.
4) Too fancy: For the most part, you should avoid excessive shadows, filters. This will allow your logo to be used across many mediums.
5) Font Issues. There are a lot of common mistakes that are frequently made when designing a logo: too many fonts, ultra thin fonts, crazy fonts, common fonts ( Times New Roman, Myriad pro, Arial).
6) Using Clipart: Create original artwork for your client and they will thank you.
7) Doesn't work in grayscale: One important thing is that they frequently will be used in strictly grayscale circumstances. (faxes, one-color prints, copies,) Logos should work in both color and black & white.
8) Bad color combination: Green tends to reflect eco, red and green means Christmas and pink is girlish. Try to match the colors to your target audience.