Does anyone know if dog boarding kennels here in Spain have to be registered and inspected by the local authority? Thank you.

Yes they do and if you take your dog to one you have to leave the Pet Passport with the owners in case there is an inspection as they will need to prove the dogs they have are correctly innoculated etc

As an extra comment there is a very good web : https://gudog.com
You punch in the town/area you want and you will find an extensive list of trained dog handlers who will look after your pet in their home. We have used it and the skill level of the handler and the home environment is much better than a conventional kennel

I owned Boarding Kennels,Cattery,Pets Cemetery for nearly 20 years in Spain.Also import/export of pets worldwideAm a registered breeder with both the British & Spanish Kennel Clubs & the British Parrot Society because I bred parrots & other species also..I can assure you that the Spanish authorities are very vigilant & registration & inspections are upheld.It is up to you,as a pet owner,to satisfy yourself that the boarding facilities are what pleases you & any good Kennels will insist you come to see them beforehand.As to leaving your pet with a neighbour/friend in their home,that again is maybe what you prefer.But remember that person is not responsible if your pet escapes or for any other problem that could arise.It happened one time to someone I knew who felt her friend would be ideal to care for her little dog.He wanted to get back to his own home,ran onto the road when the front door opened & was killed by a passing lorry.May be a chance happening but please bear that in mind if you care.