I have seen a lot of people having issues with this lesson and hope this will help some of you.
First thing you should know is that before joining your lamp parts, remember to set your timeline to 0, and set your armature to rest mode! Otherwise your model may be improperly aligned with the bones (causing floating parts or other problems.)
Second thing is that when selecting your parts to join, only the last part will keep its animation keyframes! Even Michael had this problem in the video. He joined the everything into the shade at the top, and so the base lost its jumping keyframes. If you select the base last, everything will join into the base, and the jumping keyframes will be saved.
Finally, if you followed along and made a jumping animation like Michael, your base was animated to jump, but the rig was not. When you un-parent the mesh and armature, the base will move but the rig will not, this means that the relative position of the bones to the mesh will change over the animation, causing your mesh to explode/implode as it plays.
To fix this you can re-parent the rig to your lamp. Another solution is to animate a helper object for the jumping (the rocking rotations, up/down, and foward movement.) then parent your lamp and rig to the helper. Another way of saying it is: The origin of the mesh and rig must stay in the same relative location, rotation and scale to each other. If the lamp move 1 unit forward, the rig must move 1 unit forward. If the lamp rotates 90 deg on the y axis, the rig must rotate 90 deg on the y axis.