Arnold specific settings can be attached to an object which is accessible via the Arnold Properties modifier. With an object selected in your scene, the new modifier will show up in the Modifier tab's drop-down list, and can be added anywhere in the stack:
Each roll-down group (General Properties, Displacement, etc.) has one or more Enable checkboxes, as you see below. This allows you to override the defaults on just the parts you want to control.
If multiple Arnold Properties modifiers are on the stack, the one at the top wins (as with any modifier).
If you collapse the stack the modifier will remain. However, unlike the classic object properties, the options are not properties of the object itself, the modifier must be persistent.
One of the reasons it is presented as a modifier, rather than expanding the classic Object Properties, is that the modifier allows you to better control the number of Arnold parameters, and you can copy/paste the modifier to other objects easily, and even reference them.
If the checkbox for a group label (Visibility, Shadows, General) is not On (the default), then that group is completely disabled. It is important to note that this overrides whatever the object would have by default, and does not represent the current state of the object. For the opaque flag, in particular, this can be important if you have a transparent object. It will have it's Opaque flag off and enabling this group will likely default to the opposite of what you want in this case.
The following pages describe these specific Arnold settings: