Interior.
Use a flashlight in those dark places and notice if anything has been painted to cover up something.
Use your nose and get your head inside cabinets. You can usually smell mold.
In/out:
Feel things, tap things, anything that feels soft (wet) that should be hard (dry) waves a flag.
Check for Delamination. Delamination of the exterior skin is when the glue holding the filon (smooth walls) to the underlayment lets go. Its expensive to repair and usually more than the used TT is worth.
Your choice would be to cut and patch an area and add seams or replace the entire side of the TT.