Lieberman's position as an independent candidate makes this race unique because he is the incumbent, but was unable to win the Democratic nomination for Senate. After three terms in the Senate, the primary indicated that the people of Connecticut are ready for a change. Therefore, a great deal of the debate dealt with Lieberman's record in the Senate over the last 18 years, with attacks from both Lamont and Schlesinger. Their attacks were different in both content and style, but mostly directed at the incumbent Lieberman. In contrast, Lieberman appealed to the people through his past service and did not dwell on his role as an independent candidate.
Ned Lamont had several good points and obviously is able to connect with the voters in Connecticut, but his lack of experience in national policy-making was evident in the debate. In some cases he agreed with Lieberman, but he would often take to accusing Lieberman of cooperation with President Bush or siding with the Republicans in order to portray Lieberman as a friend of the GOP. These kinds of attacks are nothing new, and are the best route when one is runnign against a successful incumbent. However, if his facts are wrong as Lieberman claims, Lamont should be careful that he is not spreading lies.  I thought his best argument was that we needed new people in Washington, and that is what he represents. If the voters in CT think there needs to be a change, he represents a strong option.
Schlesinger had the most to gain from the debate, because he is significantly trailing the other two men. This might be the reason for his passionate statements and enthusiastic responses. While Lieberman and Lamont remained calm during the debate with even speech, Schlesinger burst out and raised his voice several times. This gave him personality, but not necessarily the kind of personality you want representing you in the Senate. Because his two opponents are liberals, Schlesinger also had some opinions that differed greatly from his opponent, and he accused both candidates of poor policy during the debate. Schlesinger definitely had the most personality in the debate, with several jokes, stories and even used the "there you go again" line. However, that rhetoric will not be enough to give him a major boost.
After watching the debate, I was curious to see who was leading the race, since Lieberman had already lost the primary. Known for some more conservative stances, it is possible that Lieberman will take conservative voters away from Schlesinger and this will allow him to win the election. Here are recent poll results:
http://www.realclearpolitic s.com/epolls/2006/senate/ct /connecticut_senate_race-21 .html#polls

The average of these polls show Lieberman around 50 % and Lamont around 40%. We will see if this debate helped get more conservative voters back to Schlesinger and hurt Lieberman's numbers, since Lamont was able to present himself well against Lieberman in the debate.