Glenn - here are pix of the bad places on my machine.

your veener is chipping and lifting. You can take it off and then put on new veneer. goggle how to replace veneer, it can be done.

I know - Glenn told me it can be repaired without removing all the veneer. Using powdered wood putty and wood glue. It won't be pretty but it will be smooth. He wanted to see pictures and I couldn't get them to him any other way.

That would be a lot of putty. I would rather see you replace all the veneer on the top. The missing veneer are rather large spaces. I you want to try the putty make sure all the loose veneer aroung the edges are glue down before applying the wood filler. There is solid wood under the veneer so you might be better off to remove the veneer sand the top to make it smooth and use it this until you can put new veneer on. The veneer is oak so you easily to this yourself. You can buy oak veneer a Lowes. When the weather gets better and you can get to one and you are ready I will talk you thru it. It is not hard and you can do it your bedroom. The veneer is so loose you can scrape it off with a putty knife by pushing it under the loose veneer. Glenn

Scraping the veneer off and sanding what's left was one of the things I wondered about. I really think that's more in line with my abilities. What would you use to finish it with after removing the veneer and sanding?

After sanding smooth you may want apply a stain the same color as the rest of the cabinet so it will not stick out like a sore thumb. Then apply a couple of coats of shellac. You can also if you do not intend to put new veneer you can use a water based poly on it. you should be fine and functional. If someday you want the veneer replace the poly will have to be stripped off for the contact glue to stick.

There might be two layers of veneer an under layer going in the opposite grain of the top veneer. If this is glued tight don't worry about it. But if loose and cracked it will come off to. Look at the edge of the top with no moulding(edge where hinges are that lift the lid.) you shold be able to see the edges of the venner on the edge and where the solid wood starts.

Here's a close up of what I have. Looks like another thin sheet of something that doesn't look like veneer, then the solid top. Can't find my putty knife so I used a knife to show you. This layer appears to be loose also.

If you find that the second layer is not loose and glued down good. Glue any loose spots. It is pretty thick so should not cause you any problems. I would take the top veneer off before we decide what to do with the second layer.

Just take them both off if loose. Just look at the edge with no moulding to make sure you have wood under the two layers of veneer.