A lot, actually:
Much of the tone of discourse online is governed by the level of moderation and to what extent people are encouraged to "own" their words. When forums, message boards, and blog comment threads with more than a handful of participants are unmoderated, bad behavior follows. The appearance of one troll encourages others. Undeleted hateful or ad hominem comments are an indication that that sort of thing is allowable behavior and encourages more of the same. Those commenters who are normally respectable participants are emboldened by the uptick in bad behavior and misbehave themselves. More likely, they're discouraged from helping with the community moderation process of keeping their peers in line with social pressure. Or they stop visiting the site altogether.
Unchecked comment spam signals that the owner/moderator of the forum or blog isn't paying attention, stimulating further improper conduct. Anonymity provides commenters with immunity from being associated with their speech and actions, making the whole situation worse...how does the community punish or police someone they don't know? Very quickly, the situation is out of control and your message board is the online equivalent of South Central Los Angeles in the 1980s, inhabited by roving gangs armed with hate speech, fueled by the need for attention, making things difficult for those who wish to carry on useful conversations.