The most obvious thing I could think of would be to refrain from embossed frames, selective blurring, and other obviously computer generated effects. Placing text within the picture was certainly possible in the analog days, but too much of a hassle to be used for family photographs. If there has to be some kind of message at all, handwritten text on the border would be more authentic.
One could also emulate technical limitations of really old photographic equipment, e.g. vignetting or soft focus in the corners.