I have a Lenovo x60 Tablet Computer and when the computer screen moves the mouse starts stuttering and the t messes up when typing.. also a blue screen comes up sometimes.

Sounds like a loose lcd connector, or pinched cable.
the lcd connector is under the keyboard. remove the panel that has the power button on it, it should just pop off from one side to the other. the remove the 2 to 3 screws located at topof keyboard, plus remove 2 to 3 screws under laptop located in holesmarked with a big K maybe even circled. with keyboard out of way you will see the lcd cable connector, it should have a "paperclip" handle, pull it up then reseat the connector, reassemble and test.