You were paid to do what you could to improve the site over three months. You were never paid to totally overhaul the site in three months or less. As my favorite actor Clint Eastwood used to say in one of his Westerns "A man's got to know his limitations"
If you can discuss the shortcomings of the site intelligently and knowledgeably, you have nothing to worry about. And you shouldn't worry. Because the minute you start to worry about it, somebody is bound to think that you had something to do with that site being a disaster of a web site.
@jmort253 comments that "You could also add to this answer that avoiding placing the blame on others would be a good way to demonstrate that you're capable of remaining professional, even in the face of adversity."
My response: I didn't even think of the notion of placing the blame, because it was so obviously a legacy website. In fact, explicitly placing the blame has the unfortunate side effect of raising suspicions about you and your involvement. Why cut your nose to spite your face?