We are going to replace DB servers with mysql5.1.
Our dba team recommend that using mysql5.0 client
because, they have enough skill and know-how with mysql5.0 client.
Is there any problems in mysql5.1 server with mysql5.0 client?
The recommended would be normally to run client and server using the same major version of MySQL.
Other than that I don't really think it would be a major problem to connect a 5.0 client to a 5.1 server, it would be a much bigger problem the other way around, but be aware that your mileage may vary.