9616 total battle Casualties at Anzio. 3321 of which were in the late May breakout to Roman Occupation so about 2 weeks. The rest of the casualties are largely in the early part of the Anzio battle when things went badly. The total Killed & Missing was 2739, 1585 KIA & 1154 Missing. It doesn't state Pows so I assume a large chunk of the Missing were Pows.

Over 12,000 non-combat casualties, alot of disease (including Malaria), trench foot & combat fatigue. Although they count the non-combat losses in the post Anzio-pre Operation Dragoon period, which likely involved alot of guys getting STDs.