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That said, while the trinity force is my biggest gripe, I never downvote on one item or aspect of the guide, especially one so open to opinion. Sooooo...
The next problem I see is a complete lack of armor penetration, with the possible exception of a pittance of points from masteries. Even though your build has a defensive bias-- Which I appreciate in principle, by the by, given the sheer amount of people who don't so much as buy a negatron cloak in this game-- You're not going to be able to farm well enough and remain a threat late game except against mediocre opponents that can't lane well. With one 700 gold item, any player on the opposite team can virtually cut your damage versus them in half. Given that Riven has only a .5 second stun in her arsenal by way of crowd control, you'll be able to move around a lot and survive well, but you won't be a big enough threat to either attract attention or carry kill. Armor pen marks help with this issue, as would a Brutalizer or Youmuu's.
Next, skill order. This is again controversial for Riven, and I prefer to vary it game to game... But I've never been able to justify maxing Broken Wings first. One point is necessary, two or more early on superfluous. There are several reasons why ki burst is a better option, and the one you've probably heard excessively is *COOLDOWN!* That alone isn't sufficient reason, but it certainly factors.
Let's assume you use both broken wings and ki burst at the beginning of a given fight. At level 9, the difference is most obvious-- One skill will have just reached five points, the other two. (Assuming you dropped one point into Valor.) The combined ad ratio for both skills is 3.1; 2.1 for broken wings and 1.0 for ki burst. This doesn't change by skill rank. Broken Wings (5) + Ki Burst (2) does a combined total of 420 base damage, whereas Broken Wings (2) + Ki Burst (5) does 360. A difference of sixty damage. The difference at level 7 is fifty damage, and at level 5 it's forty damage. While up to sixty extra damage is significant, it perhaps pales compared to what one assumes the numbers would be at a glance, and THIS is where cooldown becomes important. Broken Wings ranges from 13 to 7.8 seconds in cooldown at max level, and Ki Burst from 7 to 4.2. (Depending on CDR, of course) The logic behind taking broken wings first is that the extra sixty burst makes an immediate difference... But having an extra 210 attack damage 6 to 3.6 seconds faster pushes up your dps by a very significant amount-- More so than 60 damage worth of burst. I'm probably coming off as woefully pretentious by now, so I don't wanna worsen that by throwing out words like 'opportunity cost,' but you did say yourself how dependent Riven was on her skills... And in this particular case, the cooldown makes a big difference.
Finally, a nitpick! Banshee's veil vs. force of nature. Force of Nature is less expensive, offers more magic resist, bonus move speed, and a very good amount of mid-late game sustainability via regen. Banshee's gives a slight amount of attack damage when paired with atmas due to more health, a bit of mana, and has its signature spell-negating effect. The problem here, wasted gold on mana notwithstanding, is that Riven is melee. She tends to take the brunt of the offensive spells along with the tanks in a team fight, and is sometimes even focused. The extra magic resist usually ends up making more of a difference than negating one spell, even if it IS a cc, and FoN nets you a lot more value besides. This boils down to preference often enough, but it's still worth mentioning.
Now! I've tried your build, as per your request, blow for blow in a game, and these were the major areas I felt lacking compared to my usual Riven play. I only ask that you don't dismiss my criticisms out of hand in turn. If your guide improves (to my opinion) in the future, (I check back!) then I'll gladly change my vote.