(1.) Does black and white media exposure lead people to really dream in black and white or does it lead people to erroneously report that they do?Two recent studies (Schredl et al. 2008; Murzyn 2008) cast a bit more light on these questions. Both researchers asked general questions about people's dreams and also had people answer questions about their dreams in "dream diaries" immediately upon waking in the morning.
(2.) Do people who report dreaming in color really dream in color or are the colors of most of the objects in the dreamworld unspecified? (If you have trouble conceiving of the latter, think about novels, which leave the colors of most of their objects unspecified.)
First, both studies confirm that college-age respondents these days rarely report black-and-white dreams, either when asked about their dreams in general or when completing dream diaries. Murzyn finds that older respondents (aged about 55-75 years) more commonly report black and white dreams, but even in this group the rates of reported black and white dreams (22%) don't approach the levels of 50 or 60 years ago.
On issue 1: Both Schredl and Murzyn find that people with better overall dream recall report more colored and less black and white dreaming. Schredl also finds that people with better recall of color in (waking) visual displays report more color in dreams. On the face of it, this might suggest that reports of black and white dreams come from less credible reporters; but it could just be that the kind of people who dream in black and white are the kind of people who dream less often and less vividly and are less interested in color memory tasks; or black and white dreams may generally be less detailed. Also, it's possible that the experimenters' different measures corrupt each other: People who describe themselves as having frequent colored dreams may find themselves more motivated to report richly detailed colored dreams and to try harder on color recall tasks (as if to conform to their earlier self-portrayal) than do those reporting black and white dreaming.
On issue 2: Both studies find that respondents generally claim to dream in color or a mix of color and black and white, rather than claiming to dream neither in color nor in black and white. In Murzyn's questionnaire, only one of sixty respondents claimed to dream neither in color nor black and white (which matches my own findings in 2003). In their dream diaries, Murzyn's participants described only 2% of their dreams as neither colored nor black and white. In Shredl's dream diaries, participants listed objects central to their dreams and stated if those objects were colored. By this measure, 83% of dream objects were colored (vs. 3% black and white, 15% don't recall). Therefore, if it's true that most dream objects are neither colored nor black and white, respondents themselves must not realize this, even about their own immediately past dreams. This may seem unlikely, but given the apparent inaccuracy of introspection even about current conscious experience I consider it a definite possibility.