My thoughts on various Beyond the Sword features:
The Cristo Redentor wins my prize as the thing most likely to cause me to not buy BTS. Let's see, it's blatantly unfair to spiritual civs: "Hi, now everyone can be spiritual, so where's your advantage?", and it totally breaks one of the game's major "interesting decision" mechanics by making careful use of civic swaps irrelevant. Of course, that bit about instant civic swaps is possibly even worse (assuming it's true). Hmm, let's switch to slavery/vassalage/theocracy/hereditary rule for one turn to whip some quick military units. Then to nationalism/emancipation for a few turns of drafting, then we'll go back to representation/free speech/free religion. Now if they were really stupid, perhaps that no delay in swaps allows more than one swap per turn: switch to nationalism, draft, then switch back to free speech and hit 'end of turn'. I hope not.
Ultimately, it's the kind of thing that is likely to tick me off every time I play, regardless of who builds it and whether or not it has any major impact on gameplay. Fortunately, civ4 being easy to mod means that I can probably remove it from the game in under a minute.
On the other hand, the national park (oddly enough) wins my prize for "wow, that's just the best addition". Just reading the description threw my brain into all sorts of twisty strategic thinking. I could put it in with the globe theatre for an absolute monster city. But then I couldn't put in the national epic. Or I could stack it with wall street or oxford and run lots of specialists. Or maybe even in a messy inland ironworks/industrial park city. Except that it blocks coal, but, what if I happened to not have any coal? And so on.
The Moai Statues also might be cool, especially if it goes obsolete with some popular technology (liberalism?

). Then you have the interesting choice of making a nice big early production city that won't be able to support 2 nantional wonders later on. Well designed national wonders are just plain cool additions to the game.
After waffling about corporations a bit, I've decided that they're probably going to be pretty cool and are an interesting way of dealing with all those excess resources. My one complaint is that the names mostly look pretty generic (of course I could be wrong here), which goes against the civ tradition of naming things after real world objects. I don't mind the spoof of "Standard Oil" ("Standard Ethanol") nor "Sid's Sushi", but the rest are kind of blah.
The problem with the random event idea is that there probably aren't enough to make it workable. You see, the game already has tons of "random events", starting with the world generator, which must go through literally thousands of random numbers to make a map. Then most of the AI decisions are based partly on random numbers, so some AI dropping an army on your shores is a "random event". Every time you fight a combat, there are ~10 random numbers generated. The reason all these random numbers are okay is that there are so many of them that they tend to even out. Imagine if you lost every battle you fought over the course of an entire game, even the ones that were 90% in your favor. Wouldn't that suck? With so many random numbers involved, that just isn't going to happen. You might get a run of bad or good luck, but you're not going to win or lose every battle. However, it seems like these random events are probably only going to show up a few times in a game, so there's a realistic chance of them all being negative or non-useful, or not showing up at all (or possibly favoring AI players, assuming that AIs also get shots at random events). It seems like you might end up feeling you lost or won about half your games entirely due to RNG god favor, which would be no fun at all.
The espionage additions look kinda neat and in theory ought to be good. However, I fear, at least for me, they might not be very helpful. The problem is that they are tied to the technology slider. In most games of civ, research is essential. You can't not do it. Add in the substantial benefits to getting a technology first and in my mental processes, research spending holds a designation of "vital". This means that it is only going to go out the window for something else "vital". Money to pay city upkeep is "vital", culture in order to combat massive war weariness is "vital". Emergency upgrades because somebody just drove a column of modern armor over the border and I'm still using longbows is "vital". Information gathering, routine garrison upgrades, random vandalism of enemy terriory, rush building of unnecessary buildings, and so on are
not "vital". This means the choice between technology versus other things is not an "interesting decision", it is an "already made decision". Given the popularity of the risky and not always cost effective liberalism beeline, I'd be willing to bet that I'm not the only one who tends to think of technology in this way. Now, I'm not saying that this is the correct way to play and I'm not saying that I couldn't eventually train myself to play some other way that was effective, but this is what comes naturally and if I have to go through months of retraining just to use some game feature, it's not a very interesting feature to me. I'd really rather technology weren't tied to the non-vital commerce uses, so I'd actually get to use them sometimes.
I'm eyeing some of the new units with skeptical interest. The additional anti-aircraft capabilities will be laughable unless the new intereception system makes planes actually worth building. Currently, the AI always seems to beeline rocketry and spam SAM infantry, so it just seems better to use artillery and ships to soften up city defenses. Hopefully the new anti-tank units won't ruin armored combat as well. I fear that they might render tanks pretty much useless, the way spearmen do for mounted units and SAM infantry do for air units. Things that go fast can't easily be escorted by things that go slow, meaning that they are on their own which is already a severe disadvantage. Dealing with AI tanks is usually not too difficult unless I'm only using grenadiers or something. Yea, I can take some losses if all I've got is infantry, but shouldn't going up against superior technology hurt a bit? The missile cruiser, with its need to carry limited ammunition seems to be totally counter to the spirit of Civ4. On the other hand, the paratrooper sounds like a fun addition and should lead to some interesting tactics.
I'm also holding my breath over "BetterAI", since I don't think people actually want a smart AI. I sure don't. What I want (and think they want) is a dumb AI that doesn't always make the same mistakes and have the same exploitable weaknesses. A smart AI would be no fun at all. It would be like playing against the computer at chess. At the lowest difficulty levels a chess computer may only be thinking a few moves ahead, but it never ever makes mistakes and never trys novel, interesting, or bizarre tactics, the sort of things that make a casual game of chess fun. The description of the AI as "more humanlike" gives me at least some hope that Blake was thinking the same way when he wrote the thing, but we'll see.
The scenarios also look like they could be a lot of fun and it looks like they tried to demonstrate the full power of the civ engine with them.
Last but not least, it would be totally wrong to not play Native American leader, "Chief Sitting Duck", which means I guess I'll have to buy the expansion.