When young Denny leads Sand away from the scene of their fathers death, his arm is around her waist. In the subsequent shot, it is round her shoulder.
When young Denny and Sand run out of the rainstorm into the doorway, Denny's coat is not wet.
At the poker game, Sand is holding four cards, the four Aces. In the overhead shot a black three has appeared.
The soles of The Spirit's signature Converse-style shoes switch back and forth between black and white. This is intentional and matches how Frank Miller would draw the shoes. When the bottoms are featured, they are white. Otherwise the shoes are black on black.
When Denny Colt is on the table in the morgue, you can clearly see the outline of the makeup effects around his "wounds".
During the first fight between the Spirit and the Octopus, the Octopus gets hit and apparently knocked out. He disappears into the murky muddy waters. Octopus then surfaces slowly so only a little bit of his hat and face are visible. Suddenly, his whole body surfaces with a weapon that looked like a giant wrench. He hits the Spirit between the legs with an upward motion with enough force to lift the Spirit upwards. When the Spirit lands, they're both standing on the muddy shore. In other words, after the Octopus fully emerges from the water, he's immediately standing in mud which isn't even an inch deep.
The Octopus and Silken Floss worry that if the Spirit gains possession of the Heracles vase and drinks the contents, he would become a god. The Spirit doesn't even know of the existence of the crate holding the vase, the vase, or the vase's contents. Furthermore, even if he did, there is no indication at any point in the film that he would want to drink blood out of the thing.
Despite the presence of probably over a hundred police, SWAT members and helicopter pilots who all just opened fire on him literally a minute earlier, the Octopus still grabs the vase with the blood in it out in the middle of all of these people, and somehow no one but Sand Saref apparently sees him do this.
Sand Saref blatantly using her real name at a place where she is about to commit grand larceny and coax a person to kill himself would be nonsensical enough for a master thief of her experience, but it is even worse because she purposely leaves a witness alive (the secretary).