The cassock the cardinal is wearing during the Sunday service appears incorrect. The one he's wearing may seem trimmed in a sort of purple, not the scarlet which would be worn by a Cardinal. But it's a very pinkish red if you correct the color setting on your TV set.
When Father Mulcahy storms into the mess tent after the Cardinal's arrival and Hawkeye tells him about Sturgis' leukemia, he's wearing his priest's shirt and collar under his bathrobe. Supposedly he went straight to post-op to talk to Sturgis and spent the night there. However, in post-op the next morning, he's only wearing a T-shirt under the robe. His black priest shirt earlier was not a full shirt but a collar with a fake shirt front that Mulcahy can quickly slip over his head, as was shown when the Cardinal showed up unexpectedly. This is something he can put on quickly or stuff in his pocket when he doesn't need it.