Logos's Make It So: this power seems like it will be used for one thing only: crit-spamming. Giving out natural 20s will encourage crit-focused character builds that could get pretty ugly. Especially considering the relatively light number of hit points on most Zeitgeist enemies so far, this is a recipe for really one-sided fights. The first round of *every* fight includes a crit by some striker's encounter or daily, plus whatever striker damage-booster, plus whatever crit-focused weapon they've acquired? This could get ugly fast. I would either make it a daily or change the text to "you choose whether its first attack roll hits or misses."
FWIW, Prophecy of Doom from the Divine Oracle PP does something similar (allows for an auto-crit), so I don't think this is too far fetched of a power.
Now my own notes...
-I would consider having all the powers from these paragon paths simply use "Your highest ability" instead of calling out Int, Dex, Cha, etc. That way any class can make use of these. That is the language most of the 4e powers use too, "Your highest ability". See powers like Wolfstone Frenzy and Sunspray Dance.
-Heavenly Flare: I would add your stat to damage there, seems kind of weak with just the d10.
-Applied Astronomist's Straddling Realities: I agree with Roadtoad here. Feels like a few of them need some mechanics to hang on.
-Cataclysmic Conjunction: Like Heavenly Flare, think you should add stat to damage here.
-Pathos of the Inanimate: How does this interact with items held by people? Can you pull people weapons away from them? Does this automatically let you bypass traps that you're aware of?
-Ethos of the Unwilling: I would change the text to read "to its next attack roll." instead of what is there. Just takes up less space and it is more in line with 4e language.
-Mad Shootist: The explosive gun aspect of this PP seems harsh and can leave PCs weaponless.
-Beam Shot: Roadtoad already mentioned the problems here with this power. I would also simply add that it "ignores cover" for wave beam rather than slap the restriction o nthere.
-Rocket Launcher: Want rules on rockets. Seems cool.
-Instant Boot Camp: This AP feature just seems like... it won't really see a lot of use. I'd consider scrapping it for something else. Your party wizard won't start suddenly melee attacking with a sword just because he has proficiency for a round.
-Shell Shock: Note that the entry reads Friendly Fire which is different from the power name. This and Cannon Overture seem weird to me with the flat +10, meaning it doesn't scale--maybe use ability mod? Cannon Overture needs the bit about the weapon/implement, otherwise it will be a horribly inaccurate attack.
-Crowd Effect: How long does the +5 death saving throws last? Is it always on? End of encounter? Etc, etc. Needs a duration.
-Shock and Awe: The bit about "bloodied" reads awkwardly. I would take it out, and just let it be a -2 attack penalty for each of the posse members that hit.
-Combat Focus: I don't think anything stops a PC from spamming Total Defense while out of combat and saving those extra dice for their next combat. Also, almost no one would use Total Defense in actual combat, except for a very niche build.
-Stances: Do these actually count as 'stances' since thats a term used in 4e. IE: Can a Knight use this PP and still be in their Fighter Stances?
-Polyhistor: Seems very strong overall, basic attacks have a lot going for them already.
-Close Stance: "Disarmed" is not a condition in 4e. 4e frowns upon being disarmed a lot.
-Steam and Steel: You'll probably want to make that +10 AC scale. Plate Armor for example scales by the enhancement bonus associated with it. You may want to make sure the suit scales based on the enhancement bonus of your own armor. Take a look to see how Plate scales in Heroes of the Fallen Lands (or one of the other essential books that list it).
-Steam and Steel: A larger suit is worse at climbing? Why? Seems weird to me.
-Steam Blast: Harsh penalty (standard action to get your suit going again?)
-Every Building a Welcoming Home: I would just say this gives you phasing and streamline the language.
-Every Window an Eye: Roadtoad mentioned the problems with this ability.
-Vision of the Fall: This insta-kills all minions on the board pretty much. Seems powerful.
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Overall, these are very cool, and I'm very glad I kickstarted Zeitgeist. Looking forward to the future adventures!