Getting level 2 faster – Tell your readers that level 2 = 1 full creep wave, + 1 caster minion from a 2nd wave, and that you will miss the first creep of your wave, if you leash by doing more than 1 AA + Q.
Laning: I think you’re giving too much credit to mercury’s treads. These boots are nie and they do give MR, but you are losing out on a lot of damage because you won’t get the bonus attack speed from berserker’s greaves. I think that you should elaborate on high CC lanes a little more. I’d get merc treads against some bursty lane like Taric & AP Sion, and maybe something like Morgana & Jinx, but probably not anything else. In fact, I’d probably only get cleanse to deal with morgana’s CC. -1
Early items: I don’t think you need boots of speed so early, and I think you can wait until you finish Bilgewater Cutlass until you buy boots. In terms of trading, the only thing boots will help with is running away. Vayne has some pretty nice disengage early game with Condemn and Tumble, so as long as you have decent vision, I don’t think that vayne’s ability to escape early game ganks is an issue. -3
On another note, I like how you included Hexdrinker as a situational item against APs. This item can really help you survive some bursty AP mages in mid game fights.
Warding: There are two really important times to ward. You really want to ward river around the early 2 minute marg if your opposing jungler is mobile, and stronger than your jungler. This reduces the chance that the opposing jungler will finish blue and head straight to your lane for an early game cheese. Also, you really want to have strong vision of river from the 4-5 minute mark, especially if you haven’t seen your opposing jungler gank any lanes yet. -2
Teamfights: Say something about vayne’s ability to clean up won fights. She is one of the best chasers in the game, and that it’s quite common to see a vayne start team fights way behind her tanks and end team fights very much so ahead of her own front line. -3
Try to reiterate that vayne is not good at sieging turrets herself, and that she greatly benefits from teams that excel in either diving turrets ( Renekton, Vi, Yasuo, Leona e.g.), or from team compositions that excel in sieging turrets for her( Ryze, Ziggs, Elise, Karma e.g.). -3
After the fight: You overemphasize safe play I think. If you’ve won a team fight and are at low hp would usually be a blunder since you wouldn’t be taking full advantage of your lifesteal. I don’t recall unless I need to defend, I need to buy another major item, I am low on both health and mana, or if I am low and the opposing team has someone with an assassinate capabilities ( Ace in the Hole, Requiem, Thrill of the Hunt e.g.) -3
Matchups: Post 6, twitch still has an edge on vayne in 1v1s, unless vayne can land a nice condemn. I believe twitch can win the 1v1s, so long as he gets the jump on you. If vayne starts a fight without twitch already getting the AS bonus from Ambush, vayne should win.

Another element of your guide that you could work on, is explaining how to deal with certain supports. I find that early game, supports have a very large impact on a lane, and having your guide readers know what supports can give vayne trouble, and how to deal with it, can help your readers improve their game play.

Grade: 35/50