This table was incredibly shaky when it came through my door. This is a common problem with many older pieces. The glue in the joints had broken down and was turning to dust. There is really only one good solution to that problem. (No, I didn't use screws to reinforce the joints.)
Instead, I had to completely disassemble the table, carefully breaking apart all the glue joints. I cleaned them all out, removed the remaining glue, and then re-glued everything back together.
The surface of the table was also missing some of pieces of veneer, and some of the inlayed flowers were damaged, so I had to reproduce and replace them all.
Finally, the flowered panel (below) was missing from one side of the table, so I carved a new one to match the others, and then tinted a stain to match.