The person that hides is treated as invisible with respect to all persons that failed the opposed spot check - as long as he or she does nothing to reveal his or her presence and is not spotted.
The spotting rules call for an opposed check at any opportunity that there is something to spot.
Every time you have a chance to spot something in a reactive manner
(for example, when someone tries to sneak past you while hidden, or
you move into a new area), you can make a Spot check without using an
In the case of someone using Hide in Plain Sight (HIPS) this could be any movement on the hand of the one hiding.
The observer can also actively call for a new check with a move action.
PHB, p. 84:
Trying to spot something you failed to see previously is a move action.
If the person hiding shoots this is treated as sniping. The hide check after sniping comes at a penalty of -20.
All that said it is really difficult to hide from several opponents unless your hide modifier is far beyond their spot modifiers. And it is virtually impossible to fight them and remain hidden.
A possibility not entirely covered by the rules is just moving about an area where you suspect someone invisible (or hiding in plain sight) to be. If you move into the square of the person hiding, he or she gets an attack of opportunity. The person hiding can also decide to let the person moving pass (like an ally does).
PHB p.157 (rules on overrun):
(You can always move through a square occupied by someone who lets you by.)
So far it is RAW.
What is not covered: If the person hiding lets the person moving pass - does the mover notice that there is something in the square? As a house rule in my group we agreed on a DC 25 Tumble check to avoid being noticed while letting someone pass through one's square. This is the DC of tumbling through an opponent's square.
If you run into a person hiding in plain sight it would also call for another opposed spot check to reveal the person.