The vacuum tubes I guess from your pictures are:
-
6U7G inside the round metal can on the center of the radio
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6G8G inside the round metal can to the right
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6V6G missing
From the pictures I guess the following:
I can see the radio is set to 240V input (out of 220 and 260) and the filament/cathode of the dual rectifier is tied to the two orange wires. The AC +B (high voltage) output leaves the transformer on the two green wires that are connected to the rectifier. I may be wrong, but the 6V that supplies the filaments of the other vacuum tubes leaves the transformer via the brown wire - the other leg may well be the chassis (black wires leaving the triple tie point on the transformer).
The two small capacitors (8uF and 16uF) are oddly far from the rectifier, but they are sure the +B main filter. As others suggested, I would desolder the + leg (the - leg is on the chassis) and check them thoroughly. These things tend to live a long life, but you never know.
The yellow capacitors at the bottom of the IMG_0498.jpg seem to either have been bathed in rosin or are leaking.
The charred capacitors in IMG_0500.jpg seem fine, although they are most probably wax paper capacitors that may lose capacitance over time. I would test and/or replace them.
The yellow capacitor at the right side of IMG_0500.jpg seems to have been bitten by a mouse. I would definitely replace it.
Leave the tube ceramic capacitors alone, as they have a very long life.
Also, a lot of the adjustments on these radios was done by careful positioning of the components. When desoldering, I would be very careful not to spread components too apart from their original positions.