First, it is not the paperwork, it is which paperwork
Most problems with building works start with applying for the wrong type of authorisation. A building permit (licencia), which the town hall grants after reviewing the project, is not the same as a responsible declaration (declaración responsable), which lets you start as soon as it is filed but leaves the checks for later.
The second is faster, which makes it tempting. The problem is that if the works actually needed a permit, starting with a responsible declaration does not make them legal: it turns them into unauthorised works, with proceedings opened and the site stopped.
Which one applies depends on what the works affect —structure, façade, use, floor area— and on your municipality's bylaws, which are not the same in Madrid city as in the next town.
What we check before filing anything
If the town hall does not reply
There is a widespread and very dangerous idea here: that if the deadline passes without an answer, the permit is deemed granted.
In planning law it does not work like that. The law provides that silence means refusal when the request would be contrary to the planning rules: you cannot acquire through the passage of time a right the rules do not give you. Building on the strength of a silence that does not exist ends in a demolition order.
What you can do when the town hall stalls is push through the appropriate channel, and do so leaving a record. That is casework, not waiting.
Frequently asked questions about permits
How long does a permit take?
It depends on the town hall, the type of works and whether the project is filed complete. What causes most delay are requests to correct deficiencies, and those can be avoided by reviewing the documents before filing.
My permit has been refused. Can I appeal?
Yes, and there is a deadline. The first step is to read the decision: many refusals can be remedied without going to court. What you cannot do is let the deadline pass while you think about it.
Can I start work while it is being processed?
With a responsible declaration, yes, from the moment it is correctly filed. With a permit, no: until it is granted, you have no cover.
What if I have already started without permission?
It needs looking at straight away. Depending on what has been built and how much time has passed, the options are very different, and they all get worse if the inspector arrives before the lawyer.