The principal points I have found in papal writings and in Catholic webpages, are listed in the menu to the left. But before we go into the various points of criticism, it should be remarked that the Catholic church makes a serious and fundamental error in its very definition of Freemasonry.
In their opinion, any association that calls itself Freemasonry, is Freemasonry. The RCC consistently refuses to make any difference between Masonry in different countries, rites or traditions. It defends this by appealing to the various forms of mutual recognition that exist among Masonic lodges.
Thus, for instance, if the RCC accuses Freemasons of religious indifferentism, and the Swedish Masons refute this accusation because their system is explicitly Christian, the RCC will answer that as long as Swedish Masons have friendly relations with other Masonic bodies which are not explicitly Christian, they are just as guilty of religious indifferentism because they do not condemn those who allow non-Christians to become Masons. (By the same logic, the Vatican State should be guilty of indifferentism because it has diplomatic relations with non-Christian states and recognizes them as sovereign countries.)
Some of the more fanatical Catholics I have debated this issue with have added a strange point here. When they encounter (as presented in the discussion) an association which calls itself Masonic but can be absolutely proven to be not guilty of the errors for which the RCC accuse all Freemasons, they will simply say that it is not real Freemasonry. In other words, since the RCC is always right per definition, anything which is innocent of their accusations cannot possibly be Masonic. This false logic is necessary for those whose universe rests on the absolute, unchanging infallibility of every doctrine and idea ever held by the RCC. Fortunately, few Catholics are that narrow-minded.
Beside regular international Freemasonry, there are some bodies which call themselves Freemasons and have long histories, but which deviate from the landmarks. These irregular lodges are usually recognizable by the term "Grand Orient" which they use where regular Freemasonry would say "Grand Lodge".
Regular Freemasonry has no relations with irregulars. We do not visit their lodges and we do not receive members of such lodges into our fraternity. The RCC would be able to present a more accurate criticism if they recognized this fact and did not criticize both types equally in the sweeping fashion it now does.