I have just applied for a second certificate of habitation in the Alicante region
Does anyone know what the inspector is looking for or checking when he visits the house

Why are you having to apply for second one?
Maybe it's not for the same property, so leaving that aside, any inspector will be comparing the present construction to the one originally approved when built. Also he/she will be looking for any undeclared building/construction additions to the the house since the original inspection on which more tax can be levied plus a need for approval to be sought retrospectively together with a possible fine!

See this thread for reasons why you need a second one.

As the regulations may have changed, the inspector will look at EVERY THING.

Thanks for that. I found this posting from you on the thread:-

You generally need a second habitation certificate if the first one has expired - they do after a few years. So, even for a new build where you are given a first habitation certificate, after 5 - 10 years, if you need one again, then you will need to apply for a second.
At least, this is what we have found in this area.

This is news to me although I don't doubt you for a second. Presumably, the local Town Hall will know if such a renewal is necessary?
Other than me going there and asking, what procedures are there in place for Town Halls to proactively seek renewals?
If I don't contact them, will they contact me or do they expect me to know I need renewal?

You only need to get a renewal when someone asks to see it.

In our case, we had to evict a tenant! In order to have the electricity bill (400 + euros) stay with the tenant and not the property, I had to open a new account. To do this I had to show various bits of paper including a (2nd) habitation licence as the one I had was too old. It all worked out in the end once I had the licence and shown it to Iberdrola.

So, to answer your question, I doubt there is ever a need for them to pro-actively seek one.

Thanks for that. Much obliged.