When applying your paint, it's very easy to get carried away and over brush the areas that require brushing. Brushing an area too much will cause the brush marks to become easily visible and in some cases will remove the paint which you first brushed on.
Having some kind of consistency will help when decorating your walls and ceiling and so tarting at the highest points is the best strategy as you will be able to catch drips as you work down and makes it easier to obtain the smooth finish you are after. That being said, when cutting in, only dip your brush in the paint to avoid excess paint on the brush which will drip and get wasted.
The biggest mistake you can make is not allowing your pint to dry enough between coats, always read the recommendations on the paint tin and if you are still unsure leave it 24 hours