All good points above. A few other issues, or perhaps just different way of describing already valid points.
First, I am speaking specifically in comparing the sort of income based wealth tax to a more traditional wealth tax, which places a tax on the value of wealth someone already has; such as taxes on owned real estate and the inheritance tax. Ie, assuming one chooses to create a tax to address the wealth divide, why not do it with an income based one?
Discouraging savings for less wealthy is bad
A system like this would discourage saving, the way to have the most available spending money would be to spend it every year as fast as you make it to avoid any extra tax on income. For the very wealthy perhaps your okay with this. However, look at the poor. Statistically those at a lower social-economic level have less of an understanding of economics and savings, and are more prone to spend any excess income rather then saving it. A system like this would further encourage them to do so.
However, if someone who is poor, or even middle class, runs into some hurdle, they lose their job or are disabled etc, the government will be responsible for supporting them. The less savings they have when such a disaster occurs the more they will depend on the government to assist them, thus putting more of a drain on government assistance. Furthermore, the less you have the harder it is to save money, for many reasons, so a small bump in the road for someone who is just barely middle class can put them in just enough debt to keep them in debt forever because they didn't have the savings needed to avoid that debt. Basically, discouraging middle and lower class from saving money increase later government welfare and lowers quality of life for those who lack savings. In a rational world this may not be a problem, but humans aren't always rational and a small tax based off of wealth can have a disproportionately large affect on humans tendency to save.
Though, an alternate approach to the above which had the wealth-income tax only kick in for people of a certain income or above could easily avoid this problem, because it won't discourage those who are likely to be in dangerous situations from saving.
The economy needs our rich investing
This system would also discourage people of wealth from working, since they would make so little money. Even if you didn't allow a 100%+ income tax, if it was at 95% for a wealthy individual that person may be inclined to live a life of leisure rather then working all day to make a fraction of their income. They may even go in batches, work every three years or so, spending two years living off their previous income and letting their net wealth drop so that their net worth is low enough that they don't suffer the same penalty to working.
However, these rich folk tend to hold allot of money, and their using it to invest in businesses and buy companies etc helps to drive the economy, this is part of the invisible hand of the economy. We would rather they work and lead companies and invest money so that their money can be active in our economy and helping it to grow rather then their sitting on the money in a bank account where it does far less to empower our economy. Encouraging people not to work is always a bad thing, no matter what their income, since the Invisible Hand means the more folks involved in our economy the stronger our economy likely will be.
There is a limit to how much we can tax the rich
This would also likely drive the very rich to move away from the nation that has this policy, instead living somewhere where they are taxed less, and then we loose all their taxes. This is a major issue whenever discussing any increased tax on the rich, they aren't required to stay in your nation! Admittedly this is really an issue with any sort of wealth tax, and not necessarily a problem unique to this proposal.
However, looking at the above argument from a different perspective, there is an upper cap on how much we can tax the rich before we drive them away. If we are going to put some cap on our taxes then any increase on one form of tax will be a decrease on another to stay under that cap. A wealth based income tax means we would have to charge less in the form of more traditional wealth taxes or drive away our wealthy.
The problem being that a traditional wealth tax addresses the wealth divide as well as an income based one, without discouraging the wealthy from working; thus this tax would require removing the possibility for a standard wealth tax which would potentially be better way of addressing the wealth divide.
Finally, and most cynically, good luck getting it to pass when the wealthy are the ones that 'donate' totally-not-bribes to the politicians. Money talks, and it mostly says "hey stop taxing me" ;)
Actually, I wonder about the opposite. Instead of a traditional wealth tax a tax specifically on wealth that is in savings, ie not invested in businesses or the like, to encourage the wealthy to continue spending money to drive and strengthen the economy rather then sitting back on their laurels and just living off their accumulated wealth. Though I suspect it would be nearly impossible to define a law like this that didn't have obvious loop holes and was realistic to enforce.