After the Hyatt Regency Dubai there is a parking lot, you can park your car there and right on top of you, you will see planes either approaching or climbing (of course depending on winds). Don't worry about Police here, you won't be close to the airport's perimeter.
The other place instead is on the other side of the airport, near the Mirdiff City Center. While approaching the mall you will see once again planes either approaching the runway or climbing.
[Edited 2013-04-11 13:49:53]