Detail work was damaged and missing in some sections, the veneer was water damaged and pulling up. One table had been refinished with a heavy coating of a topcoat (but I'm not sure if it was shellac, lacquer, polyurethane) but the damage to it had not been addressed and so that damage was simply cemented in. The other one in its original finish had more damage but was easier to repair, although this would come back and bite me later in the process.
Eek, pretty bad, right! So much of the veneer was pulling up on one of the shelves I decided to remove that whole panel of veneer, but it meant that I could patch the veneer elsewhere where entire removal wasn't possible, like on the top.
This may be the most boring progress shot ever, but I had never worked on these types of repairs and I'm really proud of how they turned out! Using a utility knife I cut around the damaged portions in straight lines, traced the shape onto a piece of paper to make a template, then used that to cut out a matching piece with the salvaged veneer scraps. Wood glue, clamps, wood putty, and lots of sanding make a seamless repair.
I decided to use the original knobs. I like the metallic element they add, and I even daubed gold paint onto the red portion of the design.
It was a marathon project but I'm glad I stuck with it!