You make good points, Pumpkin. Personally, though, I don't see a strong distinction between content and mechanic secrets. I think I have 2 notions about secrets (aka the elements of discovery).
1. The more difficult it is for the player to pick up on a secret naturally, the less effect it should have on the gameplay.
Basically, every time you have a secret, you're creating alternate 'timelines' for the player base: some players will know the secret and their game must be balanced. Other players won't know it, and their game must also be balanced. This can obviously multiply quadratically, which is what makes it so difficult. Note that not all pathways need to have the same balance -- it's ok to make the game a little easier if you know some secret. But the more impact on balance, the more obvious the secret should be.
2. Making use of the secret must mesh with the balance and mechanics of the game.
Number 1 is quite easy to demonstrate on Isaac's design. The secret rooms contribute a fair amount of resources to the game, and Isaac is very much a game about maximizing resources. Before you know about their existence, the game will be a little harder. After accidentally finding them once in a while, you'll eventually pick up on their pattern -- where they tend to spawn. Even if you won't consciously know where they are, you'll get a feel for it. The game will become a little bit easier then.
Isaac also has super secret rooms, which were added in one of the expansions. These rooms spawned in locations that were also had a set pattern, but were almost impossible to pick up on without learning the pattern from a wiki. Without knowing the pattern, you'd either stumble on them by accident, or find them using one of the items that lets you find secret rooms. Given the fact that super-secret rooms are often more valuable than secret rooms, the knowledge of their seeding is secret knowledge that makes a large difference to the balance of the game, but is almost impossible to pick up on without consulting a wiki. Rebirth tried to correct this issue by making their spawn pattern more predictable and easy to learn, which was correct (the alternative would have been to make it completely random, in which case there's no knowledge to learn). Unfortunately, super secret rooms are now so predictable, that they're easier to find than regular secret rooms, which I don't believe was the intent. This is a violation of the second principle, since it goes against the general balance of (at least the first) game.
Another example from Isaac is the Guppy items. Guppy items appear in Isaac in specific chests which are mostly found in the Curse room. The Curse room hurts you when you walk into it. The secret is, if you get 3 Guppy items, you achieve Guppy form, which is extremely powerful. You can fly, and you spawn tiny flies that automatically seek your enemies and for some godforsaken reason do 2x the damage of your regular tears. If you have this knowledge, you know how to achieve easy dominance of the game. But if you don't have this knowledge, you'll avoid the Curse rooms, since they hurt you and often don't give you anything good. Knowledge of this secret fundamentally changes the way you play the game from playing it *wrong* to playing it the *right* way (statistically). Not only that, without knowing this secret, you're unlikely to learn it, since you're not exposed to many Guppy items since you don't see a purpose to go into secret rooms. Serious violations of both principles here.
Here's another one from the Speluky school of bad design. (Spelunky is one of my favorite games of all time, but damn did Derek Yu try to ruin it). In Spelunky, there's a secret that allows you to make much more money on each level. Money is used both for your high score, and for buying items (assuming you haven't angered the shopkeepers, in which case you just kill them and take their loot for free). Normally, you go through each level as fast as possible, trying to gather what you can before the big bad ghost comes and kills you. This is the entire spirit of the game. However, if you're a risk taker, you can stay until the ghost arrives, and if you make the ghost pass over gems (which you deliberately left out), the ghost turns any gem it touch into a diamond, worth much more money. This is the only way to get a high score nowadays since everyone knows the secret at this point.
The problem is that in order to engage in this high risk - high reward behavior, you have to wait out the level until the ghost comes and avoid collecting gems. You basically turn the game into a waiting room, waiting for the timer to expire. This completely kills the flow of the game, and is the reason I never even try to do this, high score be damned. Worse is the fact that Spelunky HD made the original Spelunky's ghost even *slower* just to allow people to do this even more without getting hurt. This is an example of a secret encouraging the exact opposite behavior to what the game generally encourages, and hurting the game hugely in the process. Many suggestions were made to fix this issue. For example, the ghost could become faster throughout the game as it chased you, making 'ghosting' a progressively more risky endeavor. But unfortunately, Spelunky HD was released on the Xbox, where the dev got virtually no feedback, and was only ported to PC a year later, by which time Derek was not interested in changing anything in the core design.
An example of good secrets from Isaac are the effects of each item. It's fun to discover the effects over time and guess what they are rather than just be told directly. This makes the secrets part of the advanced strategy of the game. Where this doesn't work too well is with trinkets, which are passive items you can swap in and out. Once you're supposed to both figure out the effect of items and trinkets together, it becomes too complicated to know if any particular effect happens because of an item you took somewhere along the line or because of a trinket. Before I read the wiki, I couldn't figure out almost any of the trinket effects. It doesn't help that most of them are quite subtle, or only occur rarely.
Finally, an example of a great little secret from Spelunky. Long after its original release, someone found an image in the data files of the end boss looking very purple. Nobody had ever encountered this version of the boss before, so they thought it may be an unused image. At the same time, people had accidentally found that sacrificing a particular item at an altar produces an eggplant, which seemingly had no effect in the game. The idea came up that perhaps the eggplant should interact with the final boss in some way. The problem was that Spelunky has you manage the objects you carry, in the sense that you can only carry one at a time (plus specific items that go on your back). Getting to the end boss requires activating other secrets, which in turn require carrying specific items, precluding the ability to get the eggplant to the end boss. Eventually, some very resourceful gamers found the specific recipe that would allow bringing the eggplant to the final boss. Throwing the eggplant on him caused him to turn into a giant eggplant boss.
This is a great example of a minor secret with very little effect that is nevertheless almost impossible to discover. As such, it passes my first principle of secrets, and trivially passes the second one. This secret could have sat in the game for years and years before being discovered.
Inspired by this secret, Edmund tried a similar idea for the Lost in Rebirth. Finding the Lost required piecing together images from the deaths of many player characters. The whole community would need to work together to find it. Unfortunately, the whole thing got messed up when Steam achievements revealed the existence of the Lost, and data miners easily found the recipe in the data files. I personally find the Lost to be so annoying an experience, that I don't consider it a part of the real design of the game. Afterbirth is supposed to make it somewhat better but I'm still not interested in it.
