Salam aleikum wa rahmatu Llahi wa barakatu. After I did my wudu I find sometimes the presence of dust or small amount of dirt on the limbs or nails, is my wudu valid?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad, sallallaahu 'alayhi wa sallam, is His slave and Messenger.

If you are not sure when this occurred, and whether it had occurred before ablution or after it, then it should considered to having happened after ablution.

However, if you are sure that it occurred before having performed ablution and it prevented water from reaching the limbs that must be washed and you did not remove it, then some scholars, such as Shaykh ibn Taymiyyah are of view that it is forgiven and overlooked.

Nonetheless, if you suffer from whispers, then you have to repel them and not pay any attention to them as giving in to whispers leads you to a great evil.

For more benefit that small amount of dirt on body is excused in ablution and Ghusl, please refer to Fataawa 358009, 364156, 278056, 361111, 357280 and 398425.

Allah knows best.