To the best of my knowledge, the Catholic Church will recognize the baptisms of other Christian denomination who’s doctrines are generally in line with the fundamentals of overall Christian faith - Trinity, Salvation, etc. and the method of baptism - use of the Trinitarian formula, water, etc. So the acceptance is rather broad. The best official statement is found here
http://www.intratext.com/IXT/ENG0017/_P2W.HTM
which basically says a non-catholic baptism can be accepted unless there is serious reason for doubting the validity of that baptism.
The interesting fact is that the mormon church is the only one that the Catholic Church as specifically singled out by name as having an invalid baptism.
Thanks for the explanations. That helps understand the greater context.