I was taught that sincerely and faithfully were always followed by a comma; the same applies to the name (if known) and the Sir/Madam at the start of a letter.
Has the rule changed or was my predecessor just lazy?
Yes, there should be appropriate punctuation.
After the salutation, use a colon or a comma
(Dear Mr. Smith: Dear Ms. Jones,)
After the complimentary closing, use a comma
(Sincerely, Best regards, )