When Mrs Fredrick tears the page out of the notebook it shows it being torn cleanly along the imperforations and in the next scene you can see that there is now the paper above the imperforations where it would be held in the notebook spiral and then the extra paper is gone in the next scene.
When Artie is picking the lock, at no point does he turn the lock meaning the catch will remain engaged and prevent the door from opening.
Claudia says she needs a fusible link, but any wire will work, a fusible link is nothing more than a wire that acts like a fuse that prevents power overloads.
When Claudia asks Artie for a "resistor", Artie hands her something with four pins. It appears to be a glass valve (tube) with a black phenolic 4 pin base. Conventional resistors, rheostats, and varistors have two contacts, and potentiometers have three. No device that fits the description "resistor" has four contacts.