It's a huge problem for the obvious reasons. Nobody wants a country where only the rich people have a say, or have influence, or wield political power, or own all the land. Because this becomes a self-fulfilling prophecy where the rich then bend the rules to favor themselves. For example, I personally think it's ridiculous that we need a lower capital gains income tax rate to "spur investment." Investment was just fine back when capital gains rates were the same as normal income tax rates, and I see this as a way for the rich to just benefit themselves.
That said, a system where the wealthy benefit is partly intentional. The whole idea of incentivizing people to earn wealth is that the wealth should be useful. It only works if it's useful. If extra wealth doesn't allow one to buy more land, or exert more power, or gain more attention, or live more comfortably, then it's pointless and does not serve its purposes as an incentive. This is literally the entire point of it. The issue is not that it happened, it's the degree to which it happens.
My fear with #1 is that the degree of difference will be too much. This is absolutely something to keep in check. It's a tough problem to solve. But on the flip side, we don't want to throw the baby out with the bathwater. Any political or financial system that we have is going to have some inefficiencies and some disadvantages.
My fear with #2 is that people have lost the plot, and believe so firmly in "equality of outcomes" that they can't stomach any amount of inequality. Some inequality is okay! We're never going to have a completely equal world, and that's okay. I had a happy, safe, abundant middle-class upbringing, and it didn't bother me one bit that Bill Gates is a billionaire.