What happens if someone is illegitimately removed from this database?

That the someone cannot vote. But you can design system resilient to this.

How can you show whether it was a glitch, or deliberate?

Paper trail.

How do you know if the information they have about you is even right, or get it changed if you need to?

You check it. I mean, when I ask for a document I expect to receive it. And I check if it is correct, after all human error can happen anyway.

Where’s the accountability?

Every document from the state (any level) I have has a signature that indicate who is ultimately accountable for it.