There are several apps available for low-light and light trail photography. Slow Shutter! (on sale for US$0.99) is a fine example, and has been rewritten to make it easier to use and increase performance. The app has replaced complex settings with Auto mode (waterfalls, moving objects), a Light Trail mode (traffic, fireworks, moving lights) and a Night Mode for shooting in dark places.
The app supports shooting at full resolution, and you can adjust exposure when you are not in auto mode.
I gave the app a try and found it worked well. Moving water in auto mode looked quite good. Focus was pretty fast, but the darker the environment the longer a focus lock can take. About the only area where the app didn't excel was at night mode. I thought the basic iPhone camera on my 5s did very well in low light, and I didn't see much difference in noise. Both setups will make you want to have something to steady the camera against, or use something like a Gorilla Pod.