Disposers leak for four reasons:
1. The main seal fails beneath the grinding plate, water seeps down the center through the motor and drips out the bottom. Often you can feel the drips with your fingers without even looking under the unit. An easy diagnosis. Eventually the motor will either get noisy or fail. Any moisture coming out the bottom means a new disposer.
2. A hole may rot through the side of the unit or the tail pipe may rot away at the connection point. Seldom is this serviceable. Only an amateur will patch a hole.
3. The trap may rot out and leak. Replace the tail piece and trap with plastic.
4. On rare occasion an improper installation may leak at the sink adapter. A good installation will last decades. If the adapter is a standard one, and the disposer is new, a repair is possible.
Trick of the Trade: Save an unused sink adapter for situations like this.