My roommate has a Note 2 and I have a Note 3. Her charger was charging the phone very slowly and we thought it was a faulty cable so she switched it out. Now it charges fine. I just got my Note 3 today and it also charges very slowly. I think it's charged 3% in about 15 minutes plugged into the wall. Once she gets back from shooting her movie next week I will try her cable. Anyone else experience this issue with your Notes?

Well I can tell you the battery is huge so it will charge slower than most devices

Definitely could be the cable. Try a different one and see. Had the same problem with my GS3 and when I looked closely I saw that a few of the connectors were messed up. It was so bad that I would plug it in at night and the next morning it still wouldn't be fully charged. Found a old charger from my Evo LTE and now I am back in business.