Privacy will be enhanced: the individual Lightning transactions are not recorded in the blockchain, so the ledger will be more opaque than before. Surveilling all Lightning transactions would be difficult, you'd need a surveillance node in a majority of channels

Irreversibility is, in a limited way, compromised. There's an attack possible if you go offline. Some malicious user in your channel that notices you're offline can try to close the channel using out of date transactions from the channel you're both in, stealing whatever BTC they spent later back from the people they sent it to. It doesn't seem like a very easy attack to pull off with bi-directional channels, as all the other users in the same extended channel may be online to notice, even if you're not (because some of their money might be at risk from the same attempt, they're incentivised to keep watch). There's a separate protocol that's been developed to allow a third party to watch the channel for you, in the event that you're offline (or if you're not running a Bitcoin node at all), so it's not much of a risk, providing you understand it.