Water quality is the most important factor for housing diamondback terrapins, especially if they are kept in fresh water.
Diamondback terrapins are one of the most difficult North American turtles to work with. Their water needs to be kept very clean or they will develop skin problems. Normally the first sign that the water is getting too dirty is their eyes will develop a red ring around them or they might develop white patches on their skin.
I once had a diamondback terrapin in with two sawback knob map turtle. I was on a business trip for three days and when I got home I found that the filter had stopped working and the water was dirty. The sawbacks were fine but the diamondback terrapin was covered in skin fungus. It took me a while to get her back to normal. This is an good example of how easy it is for them to get sick.
The truth is they do require much cleaner water than most other turtles. Diamondback terrapins are not the best turtle for people that have never had turtles before. But with proper filtering and care they can thrive in captivity.