Reggie's husband hid the money by buying three extremely rare stamps — they were stuck to the husband's un-mailed letter the whole time. (Realization sets in when the characters go to the park on the date marked in the husband's appointment book — and see that the park is overrun with stamp collectors selling their stamps.)
Dyle, who was alive the whole time, kills off the last of his backstabbing buddies as we expected — but when he's revealed, we find he wasn't Peter Joshua (Cary Grant) but Mr. Bartholomew (Walter Matthau) the whole time.
Joshua turns out to be the U.S. official searching for the stamps the whole time and luckily for Reggie (Audrey Hepburn), single. Accepting his proposal, Reggie promises to name their children after each of the aliases he uses in this movie.
— Thanks to Ari Rottenberg!