Sahih Bukhari – Hadith no: 3461
بلغوا عني ولو آية
Convey from me even if you know one verse
The issue of judging a person to be a scholar raises several crucial points:
As Yousuf Memon said above and if you look at the courses at an Islamic University like that of Madinah or Al-Azhar there are several branches wherein a person can specialize like
However, it's important to know that having a thorough knowledge of Arabic as well as the grammar (Nahu) is vital to become a scholar who can derive and understand rulings with little difficulty from the sources of Quran and Sunnah. However, there are and were several personalities who contributed immensely to Islam like Shaikh Ahmed Deedat. What degree did he have? Such a case, therefore proves that for some areas in Islam like Daw'ah or Quran, etc degrees aren't necessary to be accepted as a scholar specialized in the respective field. However, for fields like Fiqh or Hadith, a thorough study is essentially that comes with a degree, cause nowadays study of the sciences of Hadith, etc is only taught at an institution. And after years of intensive study, the person can be called as a Muhaddith or Faqih, etc.
It is worth noting that basic rulings and fatwas can be given by many muslims even though he doesn't have a degree but has strong evidences. And if presented to the people, the people should accept it without raising issues of he being a scholar or not.
And the one who has brought the truth and [they who] believed in it -
those are the righteous. 39:33