1. Using the wrong pen or pencil.
Often people use a pen when they should be using a pencil and a pencil when they should be using a pen. Generally if you are doing outlines, comics or cartoons then a simple biro pen is fine. If you're doing caligraphy, illustration or anything to do with lettering, usually you'll want to use a fountain pen.

Another common mistake when learning how to draw or sketching is using too dark or too hard a pencil. Most people remember the old HB or Number 2 pencil from school, but don't realize what the letters and numbers mean. Well they're simply a grade of darkness. H means Hard (lighter) and B means Soft (darker). This may seem backwards but it's because the harder the lead, the finer you can sharpen the pencil without it breaking, and thus the lighter the mark. The scale goes:

9H 8H 7H 6H 5H 4H 3H 2H H F HB B 2B 3B 4B 5B 6B 7B 8B 9B
Hardest - - - - > Medium - - - - > Softest
Lightest - - - - > Normal - - - - > Darkest

This means that for technical drawings you would want a hard pencil like 4H, thus you could sharpen it very fine for light and accurate lines. It also means it's easier to rub out mistakes. For writing text an HB to 2H pencil is ideal. It's also economic, hence why the schools all stock these pencils. For sketching and shading you would use Medium to Soft range pencils.

2. Incorrect Proportions.
A very common beginners mistake is drawing the proportions of the human body (or parts of the body) wrong. The most common mistake is drawing the eyes 2/3rds of the way up the head when, if you look in the mirror, you will see that in fact they are closer to the middle of the face. The nostrils are about half the way between the eyes and the chin (so half of the half) and then finally the mouth is about half the distance between the nose and the chin (so half of the smaller half again). Hands are also commonly drawn out of proportion with the fingers, and arms too. Ensure that when learning how to draw certain parts of the body you understand and know the proportions in relation to other body parts.

3. Drawing or Sketching from Photographs.
Due to the high amount of light, flash photography will flatten a person or animals features. This gives you very little to work from and makes it hard to copy from. Many people will also take snaps of their pets or other objects to work from. More often than not this means the pet will stare up at the camera and the person will focus downward at the animal, resulting in horrible proportions. The head is much larger than the body, or is hidden from sight altogether. When taking photos of someone or something use natural lighting (take the photo during the day) and ensure that you are level with them or it. This will give you more features and lines to work from and keep everything level and in proportion.

4. Learning how to draw on the wrong paper.
Often new artists will wonder why their shaded drawing or sketch is so pale or just doesn't look right. Often it's no fault of their own and is something as simple as the paper they use. Cheap papers for example are too smooth or have a coating or sheen which means the graphite of your pencil doesn't stick to the paper and instead powder graphite has to be continually blown away and can even smudge the sketch. Another mistake is to use a notepad or notebook. Since there is padding underneath the sheet you're drawing on you need to apply less pressure incase you burst through the paper. Instead you should place your sheets of paper on a hard working surface and ensure that the paper you buy is of decent quality. The best place to go is an art store or search online. You can find hundreds of different quality and type papers for different purposes.