He expressed the view that the collapse of eastern Mediterranean Bronze Age civilisations was the result of climate change while ignoring the more extensive evidence for concurrent widespread seismic activity in the region. The most recent (August 2013) studies have again pointed to climate change as the culprit(b).
>Carpenter was impressed by Solon’s account of how the archaic Greeks lost their knowledge of writing brought from Egypt and recorded by Plato – “A remarkable detail that should convince the most sceptical of the genuineness of Solon’s conversation with the Saite priest is the latter’s unambiguous statement that the older Greek race had been reduced to an unlettered and uncivilized remnant which, like children, had to learn its letters anew. This claim we now know to be entirely exact, but we have no reason to believe that Plato himself was aware of it.”[220.33]<
In one of his books, Discontinuity in Greek Civilisation. Carpenter declared his conviction that the catastrophic destruction of Santorini was the original inspiration for Plato’s Atlantis narrative.
In another, Beyond the Pillars of Heracles  he voiced the opinion that Tartessos was not a city but the name of the river, today’s Guadalquivir, which assisted the extensive mining activities in the area.
In his 1946 work, Folk Tale, Fiction and Saga in the Homeric Epics , available online(e), “Carpenter argued(d) that the Trojan War, far from being a historical event, was in fact a synthesis of many such events involving peoples whose mutual involvement stretched back centuries.”
In 2017, Thorwald C. Franke published a short paper on the Atlantis theories of Rhys Carpenter(c), in which he noted that “Rhys Carpenter started to advocate his hypothesis since about the time of his retirement in 1955. Rhys Carpenter complained that he could not convince any of his colleagues. Here, we are allowed to see a hint to the reason why Carpenter started to advocate his hypothesis only with his retirement, and why not a single colleague agreed: Because it is harmful to a career to advocate such theses.”