While zombie processes aren't a problem in and of themselves and take up very little resources, there is one concern. Linux systems have a maximum amount of processes and thus process ID numbers. If a computer has enough zombie processes, the maximum amount is reached and new processes can't be launched.
The maximum amount of processes can be listed by typing the "cat /proc/sys/kernel/pid_max" in a Terminal window and is usually 32768. Thus, zombie processes are usually not a concern.
However, if the parent process creating zombie processes is server software that isn't written properly, a large amount of zombies could be created under load. Or, zombies could gradually accumulate over long periods of time until the maximum process limit is reached. A few zombies are nothing to worry about, but if you need to kill a lot of zombie processes, your software needs to be fixed.