The first mistake is not understanding how to take care of each plant specifically. For example, some flowers need to have the heads of the blooms taken off so they grow back stronger. Some don't need to be adjusted like this at all. Another example is that certain plants react positively when pieces are broken off or the tops are pinched a bit. This helps stimulate growth in certain areas of the plant. Not knowing how each plant works is a mistake to be avoided.
Many new gardeners end up fertilizing the plants too much. This is a huge mistake because it can harm the plants more than it helps. A light bit of fertilizer is needed to help stimulate growth, but it should not be too much.
Don't make the mistake of letting weeds take over. The problem with weeds isn't that they get in the way as much as it is that they steal the nutrients and moisture from the soil. If you are giving your plants proper fertilizer and water, the weeds are messing up this balance if you don't remove them from your garden.
Don't water infrequently, too little or too much. This is difficult for most gardeners to get the hang of. Also, be sure that the water isn't causing the soil to run off, causing excessive erosion. Over time, this exposes parts of the plant to harm or takes nutrients from your garden.
Don't go overboard with chemicals. While chemicals can make the process easier, if you get too much, the plants won't grow that well and the soil can become unhealthy. This is especially important if you are going to be eating the plants you are growing.