I've read the history section of Set Theory on wikipedia:
The next wave of excitement in set theory came around 1900, when it was discovered that Cantorian set theory gave rise to several contradictions, called antinomies or paradoxes. Bertrand Russell and Ernst Zermelo independently found the simplest and best known paradox, now called Russell's paradox: consider "the set of all sets that are not members of themselves", which leads to a contradiction since it must be a member of itself, and not a member of itself. In 1899 Cantor had himself posed the question "What is the cardinal number of the set of all sets?", and obtained a related paradox. Russell used his paradox as a theme in his 1903 review of continental mathematics in his The Principles of Mathematics.
It mentions Russell's Paradox and Cantor's question as a related problem. It seems odd to me that only this set presented a problem - mostly based on the naive heuristic which states that things present problems all the time - and which I really think is not so naive. I've done some readings on set theory books (not very deep readings though) and Russell's set is always pointed as the problematic set. Are there other sets that also presented problems?