Should I take down notes of the GD? Is it important to remember what points are being raised or to think of new issues?

It is important to remember the issues raised and the important points made - you will need this both to summarize as well as identify how you could contribute more points to the discussion. One way to remember the issues is to take notes of the discussion. However, rather than writing down verbatim or long sentences, just jot down the key words (carry a small pad to the GD). Actually, you should develop the capability to take mental notes and if you do need to jot down, limit the notes to key words. This is because, one might tend to lose track of the discussion while writing down notes. However, it may be noted here that for people who are not speaking or haven’t spoken, it might be a good practice to jot down notes, since it would demonstrate that the participant is active and involved in the discussion. It would also help one to summarize the discussion, in the eventuality of being called upon to do so by the invigilator. This is likely to happen to those who haven’t been able to speak much / at all, in the entire discussion.