Phoul doesn't live off fresh water, so I understand he wants to keep some secrets from us. But you said something about black squares? No this would be a bug if black pixels are showing in your renders.
As Attileus said, rendering bigger images and shrinking them in a paint program DOES act like antialiasing, every studio does it this way. A lot faster.
Do you render your animations in individual frames, or just in a video format? If the latter, you may get a lower quality due to some compression, depending on the video formaat.