Will the home inspection identify all of these problems ?

Answer :

Yes and No. Home Inspectors typically evaluate structural components (floors, walls, roofs, chimneys, foundations, etc.), mechanical systems (plumbing, electrical, heating/air conditioning), installed appliances and other major components of the property.
The Home Inspector standards of Practice do not require Home Inspectors to report on: wood-destroying insects, environmental contamination, pools and spas, detached structures and certain other items listed in the Offer to Purchase and Contract form.

Always ask the Home Inspector if he covers all the things which are important to you. If not, it is your responsibility to arrange for an inspection of these items by the appropriate professionals. For a description of the services to be provided by the Home Inspector (and their cost), you should read carefully the written contract which the Home Inspector must give you and which you must sign before the Home Inspection can be performed.