The main faults liable to be encountered appear to be:

Air leaks
Worn bellows' parts
Distorted parts such as bent key rods
Damaged exterior bodywork (celluloid, trim and metal fittings)
Worn moving parts such as keyboard axles and register mechanisms
Distorted parts due to long periods in unsuitable storage conditions.

 The skills required in dealing with these faults are probably mostly 'mechanical' though the expertise required when tackling larger bodywork celluloid repairs is definitely specialised.

 Since a lot of information on bodywork repairs is already in the public domain it is not intended to repeat the information here. A very useful book on the subject is 'Accordion Repairs Made Easy' by John Reuther which is published by Deffner of New York or 'The ins and outs of the accordion' by Thierry Benetoux (See 'Contacts' page).