So what checks do they do?

In the news today is the startling revelation that the alleged bomber arrested in Rome had lied about his nationality.

[...] Hussain left Italy in 1996 and arrived in the UK, where he told authorities he was Somali [he was in fact Ethiopian] in order to be naturalised as a British citizen.

Now my innocent assumption had always been that when someone applied for asylum, a comprehensive range of checks were made to ensure that they were indeed suffering persecution. What appears clear from this is that there are no checks whatsoever. If you've got the person's nationality wrong, you just can't have checked their identity or background story.