While I'm not sure without playtesting whether rewording the search rules in order to clarify the visiblile monster restriction is the way to go, some kind of houseruling is necessary either way. Searching for treasure stipulates "...you may search a room for treasure only if the room is uninhabited by monsters." This still allows for the inconsistancy where a monster can be just outside the room in an open doorway, completely visible, while a Hero searches undistubed beyond some kind of invisible barrier.
The houserule that most everyone seems to favor (my previous group included) is to combine both restrictions for all searches--no monsters may be visible in a room or corridor, and no monster may be present in the room. (The latter stipulation must be amended to include corridors as well.) This is fairly straightforward, so it's easy to see its appeal in a straightforward game like Hero Quest. As simplicity is a key trait in the game, this probably makes for the best option.
Yet among other things, forums are for exploring options and comparing experiences, so I worked up an alternate houserule to preserve the seperation of search restrictions presented in the rules. It includes part of knightkrawler's earlier idea about threatening monsters, which seems to fit its spirit, and it also addresses Goblinking's practical concerns about searching for a trap or secret door beyond an obstructing Hero in view of a monster. Only traps and secret doors searches are included, as those are location specific and can benefit from tactical placement of Heroes. For more-generalized treasure searches the "no monsters present or visible in the room" idea from the general houserule noted above works fine. Here it is:
Any trap or secret door in a room or
corridor may be searched for and
found if no monster is visible and
able to reach the Hero on its turn,
and moving to the trap or secret
door wouldn't make such a monster
visible.
I'd treat a sleeping monster seperately from a monster under a sleep spell effect, but waking rules could also work. Exceptions to such instances are judged against the wording "able to reach the Hero", which was originally included to satisfy a portion of knightkrawler's point about threatening monsters. This house rule treats nonvisible but otherwise theatening monsters differently from knightkrawler's houserule, but it could accommodate his ideas more completely by subtituting "...no monster is visible
or able to reach the Hero..."
Why all the fuss? Well, this house rule allows for secret door and trap searching behind the lines of battle. That gives less combat-ready Heroes something useful to do. Perhaps a secret door must be found to bypass an invincible threat within the room, or a special trap monster which is activated by entering a room can be deactivated by a trap search. For example, Quest notes would state a Hero (the Wizard or Elf) must take a Search for Traps action in order to read a magic book at the Alter. It banishes an attacking malevolent spirit within the room while the others keep it busy. I'm sure there's more tactical and thematic possibilities available to creative Quest makers.