Advantages:
* It's difficult to be prejudiced/biased against a poster because of who they are
* The focus is on the idea not the person who says it
* It is possible to say whatever opinion you like without repercussions
Disadvantages:
* It's easier for people to get away with contradictions
* It's easier for people to get away with for instance running away from the argument if they lose and then coming back in a different thread with the same opinions that were refuted earlier
* It's difficult to get to know a person. This means that one has to rely on the assumption of a shared culture to understand how that person thinks (not sure if this is true or not but it's an interesting idea)
* It is possible to speak in whatever tone you like without repercussions
The more anonymous the medium the more extreme the above points get.