Probably as much weight as your personal statement. Keep in mind that the secondary application will be added to your file. I know that when I would grade formal papers I would remember a student's style, their voice, and how well of a response they would craft. If another sample came through that was full of mistakes and read as if it were written by a monkey then I would get suspicious. Either the student had a REALLY bad writing day or they were cheating somehow (having someone write their assignments, etc.). While I am not saying that if you turn in a poorly written secondary application a school will toss you on the grounds of cheating, I am trying to suggest that it is a good idea to have a consistent quality of response across all of your communications. Think of it as a symphony: imagine the first number being played with passion and perfection to the point that the hair stands on the back of your neck. Now imagine the second score slightly off - the strings don't hit their mark, a horn is off key, and the beat is missed more than once. Your impression of the evening will be soured as a result of that second performance. Dental schools don't know you - you didn't grow up together or have Sunday dinners at each other's home. They are relying on your written responses and numbers to make a judgement about your intellect, level of responsibility, and ability to take on the rigors of dental school. With that said, yes, I would take the responses given on a secondary application very seriously and make sure that you are presenting yourself in the best manner possible in every correspondence with them.
Thank you for your helpful input. I was wondering about this because I just started to work on several secondaries, and I feel a little overwhelmed. I was just worried that I won't be able to do a good job on them. Thanks again.