I tried Minke whale when I was in Iceland. Unfortunately for them, they taste very good - Maybe the best meat I've tried. It's like a cross between beef and tuna but with a deep, complex (and very slightly gamey) aftertaste. It was surprisingly cheap too. In spite of this, I'm not sure I would eat it again though; while eating it, I kept getting flashbacks of a video I saw of a whale being harpooned and pulled out of…
For a 60 kg person, consumption of 100 g of whale meat with the highest concentration of Hg (i.e. MeHg) found in this study (0.49 mg/kg w.w.) would lead to an intake corresponding to 51% of the provisional tolerable weekly intake (PTWI) set by JECFA (1.6 µg/kg bw) or 63% of the tolerable weekly intake (TWI) set by EFSA (1.3 µg/kg bw)
100 grams of meat is very little as far as protein and calories are concerned, but already puts you at risk. Not safe to eat in any sufficient quantity.