I performed Hajj and when I arrived at Al-Haram (the Sacred Mosque). I performed ‘Umrah (lesser pilgrimage) and after making Tawaaf and Sa‘ee between Mounts As-Safa and Al-Marwah, I lost my companion to whom I had given all my belongings out of fear of it being damaged. The last ritual remaining was to shorten my hair, as they told us, but I did not have enough money to pay the barber. I found a man holding a pair of scissors that he handed to a pilgrim to shorten his hair with. I asked this pilgrim to shorten my hair for me. He shortened my hair but not entirely. He only cut some hairs from two or three places due to the high demand for the scissors and the overcrowding. I left and did not think that it was obligatory to cut all the hairs from my entire head, and then I did not discuss this with anybody.
After a long time, I talked to some pilgrims about what had happened to me and they told me that I had made a mistake. Was my action really a mistake? How can I correct it?

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

A Muslim should learn the rulings relevant to the act of worship which is obligatory upon him so that he could perform it with clear knowledge. Thus, the questioner was negligent in not learning the Hajj rituals before carrying them out, and he should ask Allaah The Almighty for forgiveness. As for shortening only parts of the head, there are different opinions on the issue. Maaliki and Hanbali scholars are of the opinion that shortening or cutting must cover the whole hair. Ash-Shaafi‘i said it is enough for the pilgrim to shorten three hairs. Abu Haneefah said it is obligatory to shorten a quarter of the hair.

Therefore, what you did is correct according to the scholars of the Shaafi‘i school of jurisprudence. In his book Asna Al-Mataalib, the eminent scholar Zakariyya Al-Ansaari said,

It is enough for the pilgrim to cut or shorten three hairs from the head, as removing three hairs makes it obligatory to slaughter a sacrificial animal in addition to the fact that three hairs form the minimum number of the plural [in Arabic]. Allaah The Almighty Says (what means): {With your heads shaved and [hair] shortened.} [Quran 48:27] That is, shaving and shorting hairs from your heads.

Therefore, your Hajj and ‘Umrah were accepted, if Allaah wills, and what you did was enough.

Allaah Knows best.