It's possible that bugs in the blockchain software can cause blocks to no longer be produced, essentially halting the network until the problem is resolved. So-called 51% attacks are also a failure possibility.
How will miners be paid to host apps? Given that app usage concentrates into winner take all groupings wouldn't we except the web 3 winners to be paying for the vast majority of any web 3 mining?
Bitcoin doesn't technically solve this either, its just that its data growth rate is small enough to be trivial in comparison to storage costs. Ethereum and other classical distributed ledger systems cannot fulfill the true vision of Web3 (it can and will continue to do a fraction of that vision) because they have no affectual economic functions for data rent or data handling in general. Mining/staking is paid for and everything else is an economic after-thought. Ethereum's Infura Problem is a quick way to see the consequences of these poorly suited economic incentives.
Bitcoin is about stability, but Web3 is about data, so I believe its fair to say that a distributed ledger technology built for "Web3" (which is quickly becoming a dirty word) will have its economic components focused on data. This is different from keeping the traditional Nakamoto Consensus (which judges value based on somewhat arbitrary measures) but deriving tricks to push more data - this means maintaining or exceeding the security guarantees of Nakamoto Consensus while incentivizing data routing-work and storage rather than number crunching.