In doing my homework, I have discovered a new angle to this
very convoluted procedure:
According to 30A MGL 14(2), I was correct in serving my complaint
on both the Board and the Building Department. However, according
to this rule, the Building Department is a party to the action,
which is not entitled to participate in the action until it has
made a timely motion to intervene under MRCP 24. Since the Building
Department has made no such motion, it is not permitted to oppose
my motion for judgment on the pleadings. I append the relevant 
section of the Code.

30A MGL 14(2)
(2) Service shall be made upon the agency and each party
to the agency proceeding in accordance with the Massachusetts
Rules of Civil Procedure governing service of process.
For the purpose of such service the agency upon request
shall certify to the plaintiff the names and addresses
of all such parties as disclosed by its records,
and service upon parties so certified shall be sufficient.
All parties to the proceeding before the agency shall have
the right to intervene in the proceeding for review.
The court may in its discretion permit other interested
persons to intervene.