HeroQuest's strength is its simplicity, but oversimplification can result in a bland or less-than-believable experience. Case in point: searching for secret doors or traps. Seek and Ye shall find... guaranteed, every time. Even waaaay down that hall, farther than you can move.
My bias in this case is old-school AD&D, where a tough check is needed- but unfortuanately too tough for HQ. A 1 in 6 or 2 in 6 chance of finding a secret door misses a lot of doors, or requires a lot of redundant searching on that 10' section. Why so tough? Because they're friggin' not meant to be found! Traps aren't easily discovered either- that's Gary Gygax for you.
Problem is, randomized checks would screw up many maps where you absolutely need to find a secret door to finish a Quest. In such cases a search action should automatically succeed. What about all other cases? Answer: use a check action modelled off of the Disarm A Trap action.
First-off, allow a near sure-thing die roll if the Hero is in the right place. Any adjacent space (defined orthoganally) that contains a secret door* or trap will be detected if anything but a black shield is rolled by the player on one white combat die. The dwarf doesn't even need to roll this check for traps- he should succeed automatically due to his innate trap skill.
With non-adjacent cases, bring a limit in on how far a trap or secret door can be detected when that action is taken. Use a Hero's current Mind Point total...it ain't doin' much else. A trap or secret door is only found within a range of squares equal to those Mind Points. Count the range orthogonally, as if the Hero actually legally moved that many squares (don't count diagonally).
Next, a different die result is needed to discover a trap or secret door within range, but not adjacent. Anything but a white skull will do the job. The Dwarf merely needs anything but a black shield within his Mind Point range to find a trap as he is Mr. Traps.
If you like the D&D elves-are-special slant, optionally allow the Elf to succeed with secret door searches as a Dwarf does with traps searches. After all, it was Ladril the Elf who saw Zargon's Black Hosts from afar while camping in the high passes, as described in Loretome.
One last option: Allow a Hero outside and adjacent to an open door to discover a trap just within the room that is otherwise un-discoverable. It's tougher, though. The Dwarf needs anything but a black shield, while the other Heroes need anything but a skull. Essentially, Heroes lose the adjacency advantage and are seaching with their Mind Point range.
* Regarding secret doors: Because most secret doors are located on a wall, they open to the next square and are in effect one square away. Thus, to be adjacent to a secret door, a Hero must actually be against the wall. Being at a corner (either inner or outer) alows the Hero to be adjacent to both extending wall squares.