When I first tried Vi earlier today, I was furious. I was angry that anything so OP could even come close to being released on the live servers. I've calmed down since then and while I still think Vi is ridiculously overpowered, I'm going to do my best to explain my reaction and give some suggestions so hopefully Vi can be brought to a more reasonable state.
My main problem with Vi is that there's no way to win a trade against her. Normally, when facing someone who does a lot of burst damage, the counterplay is to keep fighting after the burst. This doesn't work against Vi because the attack speed steroid and armor reduction from procing 3 stacks of Denting Blows make her even more dangerous after her initial burst. If you try to make a short trade instead, Blast Shield will mitigate most of your damage. Even if you manage to bait out her shield on a minion, Vi has 5 seconds to get to safety before the shield goes down. The combination of her burst damage, sustained damage, and shield make her too strong at trading.
On top of that, Vi's AoE lets her push too easily and gives her too much damage in team fights. If you're facing a great duelist like Poppy, at least you know that if she kills you or forces you out of lane she's going to have a lot of trouble getting the minion wave to your tower to push her advantage. Vi, on the other hand, can push minion waves almost instantly with a charged Vault Breaker and one or two Excessive Forces. And while it's bad enough that Vi can instantly burst down your AD carry in a team fight, the rest of your team shouldn't also almost die in the process from the AoE components of Excessive Force and Assault and Battery.
1. Reduce the duration of Blast Shield. In lane, 5 seconds is far too long to wait to avoid wasting abilities on a shield. A 2 or 3 second shield would give Vi more counterplay in lane but still protect her from being bursted down in team fights. The strength of the shield may also need to be reduced.
2. Remove the attack speed bonus from Denting Blows. It gives ridiculous sustained damage because it makes Denting Blows synergize too well with itself, when every other active ability on Vi's kit already applies Denting Blows and thereby contributes to sustained damage. The attack speed bonus also doesn't make intuitive sense. When you build up stacks on an enemy, the effect should be on the enemy, like Vayne's Silver Bolts. When you build up stacks on yourself, the effect should be on yourself, like Volibear's Frenzy. It makes sense that popping stacks on an enemy deals bonus damage and reduces the armor of that enemy, but it doesn't make sense to give Vi herself an attack speed boost.
3. If you want to give Vi more sustained damage, as opposed to burst, the way I'd recommend would be to eliminate the charge stockpiling mechanic from Excessive Force, but give it a slightly shorter, regular CD. This reduces Vi's burst by preventing her from using excessive force twice in a short trade, but would give her more damage over a longer engagement through more auto attack resets and more Denting Blows procs. I get the "two fists two charges" idea, but I think it's contributing to Vi's burst problem.
4. Two changes to reduce her AoE: Make Vault Breaker do reduced damage for every enemy hit, similar to Varus's Piercing Arrow, and have excessive force deal less damage to enemies that are further away, similar to Tiamat. Another option would be to further reduce Vault Breaker's damage to minions and monsters. These changes would help limit Vi's pushing and reduce some of her AoE in team fights.
The nerfs I've suggested may seem extreme, but in my opinion Vi might still be overpowered after them.
TL;DR: Vi is too good at trading and deals too much AoE damage, given her strong single target burst and sustained damage. I'd suggest nerfing her shield, attack speed steroid, and AoE damage from Vault Breaker and Excessive Force.