Shades of CHARADE?
Plot-wise, this seems like a kissin' cousin of the Cary-Audrey comedy thriller.
(SPOILER FOR BOTH FILMS FOLLOW)
Dennehy's fake cop is like Matthau's phony CIA man. Both were set up by others years earlier and left for dead, and are now taking revenge while enriching themselves with paintings/stamps.
"I think it would be fun to run a newspaper"