How to report on this...

I don’t even know where to start with this one. This picture is inside of a furnace with an older concentric type heat exchanger. Is the corrosion of the ‘flame diverter/expander plate’ detrimental to the operation or efficiency of the furnace. Anybody seen this before? Any help is appreciated. Thanks.

IMO I think it would be detrimental. Otherwise the heat is concentrated in one area and mixes with cooler air reducing the heating ability.

Recommend to client to take advantage of tax credit and get a new furnace!

Just state all furnaces require service for safe operation , And you do not see any evidence of service. service recommended. Excessive dirt noted in the chamber. How old was it? did you take a co test?
The flame does not look good in the picture

Simply a bad gas /air mix.
Recommend an HVAC guy take a look and be done with it.
He can check the exchanger.

I am guessing that if you pounded on the flue pipe there was lots of debris and maybe even streaking viewed at the seams from condensation.