Test screw length with nuts removed
With the cord terminals out of the way and the nut removed, test inserting the screw through the appliance terminal. Does the screw go in easily and contact the appliance terminal? If so then the screw length is OK. (Threads on the screw and/or nut may still be damaged, but at least you'll know whether the length is good.)
Turn the cord terminals over
Look at the picture below. Notice that the appliance terminals are rotated so that the crimp is "up" ie facing the viewer. The crimps on the cord are facing "down" away from the viewer. Because the crimps stand proud of the terminal face they may be hitting the plastic barrier piece and preventing the screw from being tightened correctly. Twist each conductor 180 degrees to eliminate the interference between the crimp and the plastic.
Replacing the hardware
If you do decide to replace screws and/or nuts, be aware that it's easy to make a mistake. When you have your final selection, ensure that the nut spins onto the screw easily (that the thread pitch is correct) and also ensure that the screw doesn't wobble in the nut (ie, that the screw's diameter is correct). It's easy to get an 8-32 screw and a 10-32 nut, for example, but the combination won't hold reliably.