Vayne Mechanics
Wall of text incoming. There is no TL;DR.
I think Vayne is a great champion design. I also think she's perma-banned and needs a small change to her mechanics to remove that label.
I love Vayne's passive, I think it makes her a great chaser.
I think her Q, Tumble, is really interesting mechanically, making for an evasion tool, both with and without ultimate. It's an AA timer reset and an enhance auto, but the tumble delay timer makes that not even bad, since tumbling reduces her damage at higher attack speeds unless she's using it to close. Even better, it can't cross permanent terrain, so it isn't an escape for someone so necessary to pin down and kill. (Though, passive through Trundle pillar, Jarvan pit, and Anivia wall is a questionable choice in my opinion.)
W, Silver Bolts, is a great mechanic making her a tank killer and a cleanup machine along with her passive and tumble. She has the tools to close that little bit of distance for the last hit, but the three hit requirement gives time to CC and nuke her before she gets it off, in theory. I will explain further down why that's a theory and also not a significant form of counter-play.
E, Condemn, is my least favorite of her abilities, but still a strong addition to her kit. It is the one I would like to see most change, but also the one that gives her dueling, kiting, and escaping potential. This is both good and bad, primarily because a hyper-carry with hard CC like a 1.5 second stun (something not even softer carries like Jax, Annie, or Riven or hard-line supports like Bard, Taric, or Leona can get at level 1 or ever in some cases) is amazing. *Note: I use "softer carries" as a relative term, since % max health true damage is the hardest carry known to man.
Finally, her ultimate, Final Hour, is both great and mediocre. With skill, the invisibility on Tumble makes you unstoppable, but without the unpredictability you need, it's a lackluster gimmick. The AD and additional movement speed are nice, but not usually why the ultimate gets used, in my experience.
Now, above I said you have a chance to CC and burst her. I also said that isn't significant counter-play. My reasoning is that removing someone's ability to play until they're dead is the counter to everything. Being able to dodge a skillshot or outplay a movement ability or trivialize CC are significant counter-play. Vayne has no skillshots; her movement ability isn't an escape, it's a kite, close, or dodge; her CC is avoidable, but is incredibly strong, stemming from the range of activation, the range of knockback, and the duration. I will expand upon Condemn's mechanics below.
As I stated above, Vayne's passive and Q are great. In fact, I think Tumble should have a shorter cooldown at lower ranks, maintain the buff for less duration, and do about double the damage it does now. It would make kiting, chasing, and AD scaling all better for Vayne.
I have three major complaints and two minor complaints about Vayne's kit.
Major Complaint #1: (An early game nerf) Silver Bolts, the identifying mechanic of Vayne and her primary damage tool, only scales off two things: Attack Speed and Ability Rank. One of the most consistently damaging abilities in the game (debatably better than Fiora's % max health true damage, which requires her ult activation or a vital to pop up, though the % can be higher, BUT IT SCALES WITH AD) requires no AD and no Critical Chance.
Blade of the Ruined King, Devourer, Phantom Dancer, Statick Shiv, and Berserker's Greaves are her favorite items, and only one of those has AD (only 25) and two of them have Critical Chance, all of which is just icing. With a Blade of the Ruined King, Berserker's Greaves, and 4 Recurve Bows, a total cost of 8600g (something you can get from about 100 cs and being in the game for about 5 minutes) you can have max attack speed (with innate bonus attack speed), dealing 327 base AD + 75 AD + 24% current health physical damage + 8% max health true damage per second (or 83% of that, accounting for the 2.5 attacks per second) at level 9. You don't even need to be winning, you can do this from way behind. Getting kills just hastens the process.
My point is, Silver Bolts needs to scale off something other than attack speed. If it were 1%/2.25%/3.5%/4.75%/6% +.5% per 100 AD, she'd have an actual incentive to build AD and still have around 8% at max rank and full build. Hell, if you halved that scaling and allowed it to critically strike, you could encourage her to build Infinity Edge and actually need to have just NOT lost in the early game to be the hypercarry she wants to be. It would also make her early game actually weak, making her capable of being shut down (4% max health at level 1, 2, or 3 is a huge advantage, since no runes, masteries, or items can help you).
Major Complaint #2: (A change) Condemn has a point-and-click .5s knockback with a potential 1.5s stun. This is gauranteed peel, disengage, or kite, with potential CC. It also applies Silver Bolts without interrupting autoattack timer. I love the idea behind it. It's thematically perfect for Vayne. Mechanically, it's incredibly misplaced and has only one counterplay: don't stand near terrain and save your gap closer. Unfortunately, it can knock you completely out of range of Vayne, as its knockback distance is the same whether you're right next to her or at max range (which I'll get to in a second). This makes her kiting incredibly strong, when the rest of her kit screams for her to chase, not run.
Regarding range, it matches her autoattack range, not only distance-wise but functionally, being calculated by hitbox edges like an attack. If she can auto you, she can Condemn you. She doesn't even have to move into a more dangerous position to use it. At max range, if she nails you to a wall and is using it to escape, she is successful, because it has 1.5 to 2 seconds of disable. This makes a short-range, low-health, supposedly-weak-laning late game hypercarry much safer in the early game than seems appropriate when combined with a short distance, short cooldown movement ability.
Condemn needs different functionality. I think Condemn should be a straight line skillshot. however, I think it should not only keep it's maximum range but ALWAYS USE IT. The caveat being that the maximum range is always the distance the skillshot travelled plus the distance the knockback moves the target. If Vayne lands a maximum range Condemn, the target should only move a little, but if she Condemns from point blank range, the target will move a lot, increasing the chance of a stun. I think its targetted range should be maintained, however, so that getting the full distance means the target is moving away or used a flash. This adds counter-play in two ways: Skillshots are innately counterable and baiting the Condemn before fully engaging reduces the chance for a stun (because her Tumble will be less important in the angle at longer range). Finally, if Vayne Condemns you, but you flash before it connects, you don't knockback as far, meaning your flash is less likely to be wasted.
Naturally, I don't even know if this is possible with Riot's skillshot or knockback systems.
Minor Complaint #1: (A buff) With the addition of more options for mobility for traditionally slow builds (mages with Luden's Echo and tanks with Deadman's Plate), Vayne's passive quickly becomes irrelevant because the 30 movement speed does not scale (although I do believe it gets multiplied by % movespeed bonuses). This could be solved by giving it a per-level scaling or baking a scaling into leveling her ult (I am a fan of the latter).
Minor Complaint #2: (A buff) Tumble locks out autoattacks during the movement. For someone so nimble as to turn invisible when they roll around, she sure takes a long time rolling. Tumble becomes just a dash rather than a damage tool at later levels and builds, interrupting faster autoattacks for 50% bonus AD when she could instead ignore the "autoattack timer reset" (which it technically is but does a poor job of by being so slow) and proc her Silver Bolts faster. Her roll animation needs to be faster or the reset needs to happen at the beginning and she needs to be allowed to auto while rolling, possibly also consuming the buff.
Minor Complaint #3: (A nerf) She's instantly invisible for 1 second. I think it should be .25 or .5 seconds. As stated above, her safety is currently far higher than I think it should be, and the ability to ult and turn invisible every 2 seconds (with an immediate autoattack, 8 seconds or less without) for 1 second makes sticking to her and getting the only current counter play (of CC until dead) that much more difficult.