What are the limitations on catching pokemon in the Pokemon Dream World?

Their was originally a 50 pokemon limit in the NA version, but it has since been removed:

At some point in 2010, the limit that meant that players could only ever send 50 Pokémon from the Friend Board was removed.

No, you are able to continue to get as many pokemon as you wish. However, you can only store 50 pokemon on the board in the dreamworls. It acts as a pokemon box so once that is full, you will not be able to go to the forest to recruit more friends. What you do, is you send the pokemon from the dream world, over to the entralink, where the pokemon can now be in your black or white copy. However, it is important to note, that eventually you will run out of room, when you have filled all your boxes and the dream world billboard. So only keep pokemon that you really need or want. hopes this helps!