It depends on what you consider problems. I have heard that clutches and CV joints (front halfshafts) get 60,000 miles. Spark plug wires and valve cover gaskets get about the same. My clutch has 96K on it so I guess it depends on how you treat it.
Some automatic transmissions have problems early on, but that kind of depends on how they are treated and if they were well maintained.
I think that the engines are among the best in the business. They are over-engineered from what I have read.
The rest of the mechanicals and interior bits also hold up very well.
If you are interested in reading about the mechanicals, I can refer you to the Ergon-ITE site about the KL-series engine and FAQ on the 2nd gen MX-6 and Probe GT. It has a wealth of information on these cars.
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