Computer desk vibrates and hits wall while I type, need solution?

It's either that all the feet are not taking equal load or the table has slack in the connections. If it's the feet issue, the plastic feet ARE adjustable, they are screwed in and you unscrew them to make a leg longer. If that issue is ruled out then it's the connections of the table, it simply isn't built to tight enough tolerances. Then, attaching to the wall is working solution.

Extending from Ack's suggestion would be to jack up two of the legs (front pair) to cause the table to cant rearward. The amount should be the minimum necessary to get the edge of the table to rest against the wall.

Place a gel pack of some sort between the wall and the table edge. I have a gel mouse pad which is overkill for this type of application. Even a silicone mat with sufficient bounce would absorb the vibration from typing and may also be easier to find.

Amazon has pet food mats which appear to be well suited:

as they are relatively thin, but thick enough to absorb the vibration. Use tape to attach the mat to the desktop and let it hang over the edge. You could get away without shimming the table legs if the mat is soft enough.