In my opinion the small arrow beside each layer in the ArcGIS Online mapping interface is not a well thought out design. The small drop-down button exposes ~20 layer options which are highly useful yet hidden and not easily accessible when configuring your map. Frequently used options should be available in other ways such as a layer properties tab, on the toolbar, or on a context specific ribbon. A right-click menu does not improve the current design, but offers anther way to access tools and properties. Being able to access options in more then one way is important for efficient use and is already a common trend in other products of the ArcGIS platform.