It is obligatory to remove anything that may prevent water from reaching the skin, but one is forgiven for a very small amount such as dirt under the fingernails or in cracks in the feet, after trying hard to remove it.

If a person does Wudu and washes his hands, then rinses his mouth and nose, and washes his face, then he washes his arms from the wrists to the elbows, his Wudu is not valid according to most of the scholars.