I would agree that letting a new employee know what your standards are is a very good idea. However, nothing is to be gained by trashing the previous employee. A new person only needs to know what you expect from him or her; they don't need to know the failings of their predecessor.

Do not say anything about the previous employee. Show the newcomer what you want. This would be a great opportunity for you and the new employee to produce a 'desk book" or procedures manual. The new employee could refer to it and add to it or update as necessary, and if the new employee didn't "work out" you would have the desk book available for his/her successor.

I agree you shouldn't mention the former employee. Aside from all else that has been said, another piece of starting an employee out on the right foot is demonstrating how you treat each other. Bad mouthing or in any way talking about the former employee in a negative way may leave the impression that you aren't all that nice to each other and perhaps not very professional.

Set clear expectations and move forward from there. Don't dwell on the past by discussing the former employee (I'm not saying you're dwelling, but remember that first impressions go both ways and that may very well be the impression you leave). Move forward with a new employee, a new start, and all of the positive opportunity that exists in this new employment relationship.

I agree with Lynn. I would suggest the same thing for the same reasons.