Some perks are visible to your rivals. Some aren't. Being visible to your rivals is only a downside of a perk if they notice (or could notice) and it's a thing you don't want them to know. All perks can be revealed in the game through Dark Augury. Your thoughts?
Master Archer, Master of the Sword, Sorceror: Only visible if you have at least one point in the relevant stat i.e. if you're using it at all. It seems a little silly, but I could imagine for example, starting with 0 Wickedness and Sorceror so that people didn't realize you had a legion buffing perk right away. Check out the strongholds. They're supposed to have combat stats totaling rank+5 (eg a Duke's stronghold has stats that total 9.) If they have too much, it's from one or more of these perks. There's some nuance to this. If there's 3 points too many and the stronghold or legion has Ranged 2, then you know it's not +3 from Master Archer, but it could hypothetically still be +1 from Master Archer and +2 from Sorceror. If they capture a PoP, those all have known stats, so it should be easy to figure out what bonuses they're getting. When the bonuses are known, this also broadcasts your stat.
Inspirational Leader: Visible when you have a non-bodyguard legion. The legions have known stats, although they can be changed after acquired. If you check a legion the first turn it is under your rival's control, it should show the presence of this perk, and the rival's charisma at that time.
Fiendish Energy, Slothful: Visible. These are both really important to know about and easy to spot.
Marked with Evil: I've never tried this perk, but if I understand it right, it could only become apparent when the +2 bonus applies on top of a combat roll of 5 or 6. When it looks like your enemy's legion rolled a 7 or 8, that's really what it is. Certain praetors, artifacts, and Infernal Juggernaut also boost the legion's roll, so don't forget to count those in. This will only be visible to the opponent involved in the combat, and only if they look at the combat screen and crunch the numbers.
Infernal Warlord: Visible if someone else can calculate what your command rating should be without it, and you are exceeding that command rating.
War Master: Visible when you use it, but so much more subtle than I realized at first. I once had a legion with multiple attachment slots. I had Martial Skill 4. I did not have War Master. I had a single combat card attached to that legion. I wanted to make an attack, but I knew I would need slightly more bonus to succeed. So in phase 1, I created a second combat card (with only one effect) and in phase 2, I attacked. The strength of the combat card revealed my Martial Skill (at the time I made the card.) My Martial Skill 4 revealed that my combat cards should have 2 effects each. My opponent had seen that I had a single combat card on that legion, but then he saw 3 effects from combat cards on the combat screen, if he checked. If I had seen that, I certainly would have assumed my opponent had War Master. I didn't have it.
Ichor of Rejuvenation: Martial Skill, Intellect, and some relics also contribute to Healing Rate, which can be visible when you use it. Because so many things increase HR, it's often hard to tell why a particular fiend has a particular HR. Sometimes, only some of your opponents will know how much your legion was damaged, and therefore how much it healed.
Infernal Cardinal, Obscure, Devoted Minions, Collector of Curiosities: Not visible.
Monumental Vanity: Visible when you are using it. Your +prestige per turn on your avatar screen (visible to everyone through Diplomacy tab) will differ from your total on the map. Your stronghold does not count as a PoP for this perk.
Glory in Battle, Arena Gambler, Bully: These all produce prestige when a certain thing happens. All of those things normally change your prestige total anyway. There are invisible sources of prestige, to make it even harder to tell.
Debauched: Invisible. Perhaps the only redeeming quality of this crippling perk.
Unnatural Prescience: Pretty much invisible. Even when you use multiple events at once, it should generally be unclear who played them.
Saturated Ichor, Prince of Lies, Seer, Harbinger, Paranoid, Iron Tower of the Mind, Tough: Not visible. An unexpected pattern of success or failure in a particular school of rituals can provide some evidence of these perks, but no single incident really proves it. Paranoid in particular can be good to have known. If you can convince a Deception guy to put you on the bottom of his threat list because he'll fail a lot of his Looting the Vaults against you, he may never Loot you.
Playing For Keeps: Visible when you use it, if anyone has been counting vendettas. Could be useful to document the fact that you have only won two vendettas against a particular target before declaring Blood Feud if you want it known.
Master Administrator: Visible. I'll have to try it some time.
Power Behind the Throne, King Maker: Invisible. That's the whole point, really. They only appear when the winner is decided, and only then when it's decided by prestige.