Revealing mistake: In the last scene of the film where the Reverend is holding up the glass jar with the mini-blob in it, you can see the mechanism being used to move the blob (look between the Reverend's fingers). (01:30:30)
Other mistake: We know that the blob dissolves flesh and hair and that it can also burn wood (since fluid coming from the blob burns a small spot on the desk in the hospital) and that it can dissolve bullets, but despite this obvious acidic state, the blob doesn't dissolve plants, walls, glass, concrete, metal, nor sticks and twigs.
Suggested correction: It can control its functions otherwise it wouldn't be able to exist.
Revealing mistake: When the Blob is eating Paul at the doctors office, his right arm is the only part not covered. It's very obvious that it's in a fixed plastic sleeve surrounded by the Blob's ooze.
Continuity mistake: When poor George is about to be sucked down the drain by the blob, he is looking at his hand. When the blob attacks him, he's holding on to the sink with both hands.
Other mistake: The Blob hates the cold - it backed out of the freezer and it backed away each time someone blasted it with a fire extinguisher, but it enters a theater's air conditioning system with the air on at full blast this should have made the vents too cold for the blob to continue further.
Revealing mistake: When Vicki is comatose while The Blob is inside her, you can see her blink despite her already being presumably dead.
Continuity mistake: When Paul calls Sheriff Herb, the window is closed. Who opened it for the blob to escape?
Continuity mistake: After Meg and Kevin climb the sewer pipe that leads to the street, Meg is unable to fit in the grate. In one shot she's trying to fit her head through the grate but in the next shot she is not. (01:12:22)
Revealing mistake: The scene where Meg fights off the blob using a fire extinguisher isn't composited well. The blob and the street light are translucent. The street light even disappears when it's knocked down.