AFTER our recent sightings of an assortment of European princes, dukes and barons at the socially desirable soirees around town, Keeping Posted now gets down to some serious titles. Spotted at hip-hot JJ's was Prince Joachim of Denmark, second son of Queen Margrethe, who is spending a few months in Hong Kong getting work experience with a Danish shipping company. On his return home, 27-year-old Joachim is expected to become a full-time farmer, as he has recently inherited a large farm in the south of Denmark. (Elder brother Prince Frederik, of course, will inherit the whole of Denmark at some future date.) Also in our midst is Prince Philippe of Belgium, whose father is King Albert II. Philippe is said to be on a ''strict private visit'', although we know he is scheduled to visit a well-known tailor of our acquaintance.