My approach to detecting secret doors is the same as my approach to detecting traps: description. The players listen to my description of their surroundings, then they describe what their characters do to search for them. If a secret door is in their vicinity and their efforts fail to reveal it, then I secretly roll for their chance to detect it. This represents a second chance to notice something they have overlooked.
I realize this is the opposite of the method used by many groups. Standard practice is for the players to declare that they are searching a particular 10' by 10' area. For each such area searched, the referee makes a roll for each player character who is actively searching. That's all there is to it. It takes 1 turn per 10' by 10' area searched, so the only thing preventing a party from inspecting every foot of a dungeon (and making hundreds of secret door rolls) is time and Wandering Monsters. This might be considered reasonable from an archaeologist's point of view, but from the adventurer's perspective, as a player or a character, this could be rather boring.
Allowing player characters the ability to search quickly in this manner (perhaps 1 round per 10' by 10' area) is not the answer. Sure, they might encounter fewer monsters and use fewer torches as they conduct speed searches, but they're still just telling the referee, "I search this area," and listening to the referee roll dice. One could literally check for secret doors at full running speed in Wolfenstein 3D, and guess what? It was boring (searching for secret doors, that is).
Even using the descriptive method can be boring if the referee doesn't provide details that are conducive to initiating a search. Tracks that end at walls and sounds heard in rooms where there is no egress other than the door through which the adventurers entered are good indications that there may be secret doors. Sometimes the secret door can be fairly obvious, but the means of opening it is the real puzzle. Ultimately, the best use of secret doors is one that encourages player characters to explore with a sense of purpose rather than a feeling that they need to painstakingly inspect every 10' square surface of their environment, unless that's how your group gets its kicks. Otherwise, use sparingly and never randomly.
[In retrospect, I think Secret Door Techniques was my inspiration for writing this. Read ye, read ye.]