How to trigger Mouse-Over on iPhone?
Mobile Safari has no mouse and hover events (at least not in the usual accepted sense), they are explicitly called out in Creating Compatible Web Content Unsupported iPhone OS Technologies:
Mouse-over events The user cannot “mouse-over” a nonclickable element on iPhone OS. The element must be clickable for a mouseover event to occur as described in “One-Finger Events.”
Hover styles Since a mouseover event is sent only before a mousedown event, hover styles are displayed only if the user touches and holds a clickable element with a hover style. Read “Handling Events” for all the events generated by gestures on iPhone OS.
The answer is in the documentation that Remus posted. If you add an onclick = "void(0)" declaration, you will instruct Mobile Safari that the element is clickable, and you will gain access to the mouseover event on that element.
More info here
I think you need to reconsider your design for the iPhone (and any mobile for that matter). iPhone web interfaces shouldn't depend on mouse-overs and hovers, as they just complicate the interface significantly.
I strongly recommend that you design a new interface that is optimized for mobile viewing, that don't require clicking on small tiny arrows just to show more options.