Revealing mistake: When the one twin rips the man's arm off, the arm he is holding is not an entire arm, but more like 2/3 of an arm. It is ripped off slightly above the elbow. But in the next shot, you see the man is missing his entire arm almost up to the shoulder.
Deliberate mistake: There is no way Ichi's blade could have cut the one man vertically in half, as shown in the movie. The blade is only a couple of inches long, not nearly enough to slice through the man. When we see the blade shooting through the back of him, it is obviously a different, longer blade.
Revealing mistake: After the girl has her nipples sliced off (in the uncut edition) in some of the shots where you see her dead body, you can tell her nipples are obviously still there, just being disguised (poorly) with makeup.
Deliberate mistake: When Suzuki has the boiling oil poured over his body, his skin doesn't react quite realistic. You only see it scar up a little bit, when realistically, the heat would be melting the skin right off.