3. Stacking more than one filter or lens hood
Make sure you don’t put your circular polarizer on top of a UV filter, or leave the lens hood on at the same time.
4. Shooting at wide aperture
Similar to taking a general landscape photo, you want to choose an aperture of f/8 or smaller when using a polarizer. If you choose a larger aperture, you might see some vignetting or light bands in the sky. So stop down to f/8 or smaller, the vignetting will likely disappear. See following bad example. ISO125, 16mm, f/5.6, 1/320sec
5. Using a circular polarizer that isn’t thin enough for a wide angle lens.
So far all my lens filters are either from B+W or Lee. I found these two brands very reliable. They are also pretty thin for my wide angle lenses. Make sure you study the features of the glass before you purchase, if you choose other brands.
Last but not least, using circular polarizer is not limited to the above scenario. In fact I find it most useful to use a polarizer when photographing waterfalls, creeks, or rivers in the sunlight. You can reduce the reflection of the wet rocks nearby and create a more visually pleasant image. The following are two photos I took at Bruarfoss in Iceland. You can see the difference on the bottom right corner of the rocks.