One problem related to catalytic convertor has been reported for the 1996 Honda Accord. The most recently reported issues are listed below.
When accelerating, the exhaust system makes a loud vibrating noise, which Honda service attributes to a problem with "torque". Service rep. Claims it happens over time, and Honda makes a "buzz kit" for the problem. If it is already a known problem by the manufacturer, then replacement or repair should be at no cost to the owner.