Reproduction steps:

1. Create a new Unity project.
2. Click on the hierarchy with the right mouse button.
3. Select: UI > Dropdown.
4. Save the scene.
5. Build the saved scene for iOS or WebGL and launch the application.
6. Touch the dropdown list.
7. Try to select and unselect elements of the list.
- Elements are unselectable on iOS.
8 Try to close/shrink the list.
- List doesn't close on iOS and WebGL.

Reproduced with:
[iOS]
5.2.5f1, 5.6.0b8
iPhone 7+ iOS 10.2
IL2CPP, Mono2x
[webGL]
Chrome 56.0, Safari 10.0.3, Firefox 51.0.1

Not reproducible with:
Editor, OSX standalone, Android

Note:
Errors are thrown into an Xcode console (attached in the edit):

"NullReferenceException: A null value was found where an object instance was required.
at UnityEngine.UI.Dropdown.SetAlpha (Single alpha) [0x00000] in <filename unknown>:0
at UnityEngine.UI.Dropdown.Hide () [0x00000] in <filename unknown>:0
at ...
...
...
"

Workaround:
Disable "Strip Engine Code" in the Player Settings.