Early in the film, Dr. Deemer goes into the lab and puts on his apron, he is wearing a shirt with short sleeves, but when he puts his arms in the isolation box, the sleeves are long, like a lab coat, then short again in the wide shot when he pulls his arms out.
When the Tarantula attacks Prof. Deemers house we see a closeup of its "face" looking through the window, with two large eyes right above the jaws. A real tarantula looks completely different, with eight eyes, located at a very different position.
At the tarantula's final size, humans would no longer be a suitable prey for it since more energy would be expended catching and eating such a (relatively) small food source than would be gained from ingesting it.
Prof Deemer takes special care to fill the hypodermic needle inside an isolation box wearing rubber gloves. However, once it is filled he pulls it out of the box with his bare hands and then removes air from the needle by shooting a little bit of serum out. Had the toxicity of the serum been that dangerous he probably would have done that with the needle still in the box and would have worn gloves while handling the needle outside the box.
When Prof Deemer inspects the animals in his cages he changes the card (on the clipboard) showing the age of the first animal (white rat) from 5 to 6 days and writes that the rat received the second injection on the 6th day. However, even though he is holding the needle in his hand, he does not give the rat an injection. He then inspects the clipboards for the remaining animals yet does not change the date of the age for any of them.