PREDIMED was a recently-completed massive randomized controlled trial testing the efficacy of the Mediterranean diet for improving heart disease endpoints. The Mediterranean diet differs from a traditionally recommended low-fat diet in that it emphasizes "good fats" - especially olive oil, nuts, and seafood.
The experimental design of this study had three arms. The first arm ate a Mediterranean diet with an emphasis on extra virgin olive oil. The second arm followed a Mediterranean diet with mixed nuts. The third arm served as the control group. This control arm was instructed to eat a prudent low-fat diet.
Unfortunately, the control group failed to substantially reduce its fat intake. Nevertheless, there was a statistically significant difference in total fat intake between the Mediterranean and control groups (41% vs 37% of total energy from dietary fat). The low-fat hypothesis would therefore predict a lower risk of heart troubles in the control group, but that's not what happened. The low-fat group actually experienced a higher risk than both Mediterranean groups (primarily from stroke).
Some have said the study was flawed because the control group ate a typical Western diet. But upon reading the actual data (Table S5), I found this claim to be false. By the end of the study, 60% of the control group was getting 5+ daily servings of fruits or vegetables, 97% was eating less than 1 serving of red meat per day, and 94% drinking less than 1 serving of soda each day. And 66% of the control group ate at least 3 servings of fish or seafood per week. This isn't what the typical Western dietary pattern looks like.
An earlier paper on PREDIMED also found that both Mediterranean groups had a lower risk of type 2 diabetes relative to the control group.
A blogger named Kismet has a great summary of all the questions and criticisms related to this trial.