A machine may crash while it is delivering a message. For both mbox files and mh folders this means that the message will be silently truncated. Even worse: for mbox format, if the message is truncated in the middle of a line, it will be silently joined to the next message. The mail transport agent will try again later to deliver the message, but it is unacceptable that a corrupted message should show up at all. In maildir, every message is guaranteed complete upon delivery.
A machine may have two programs simultaneously delivering mail to the same user. The mbox and mh formats require the programs to update a single central file. If the programs do not use some locking mechanism, the central file will be corrupted. There are several mbox and mh locking mechanisms, none of which work portably and reliably. In contrast, in maildir, no locks are ever necessary. Different delivery processes never touch the same file.
A user may try to delete messages from his mailbox at the same moment that the machine delivers a new message. For mbox and mh formats, the user's mail-reading program must know what locking mechanism the mail-delivery programs use. In contrast, in maildir, any delivered message can be safely updated or deleted by a mail-reading program.
Many sites use Sun's Network Failure System (NFS), presumably because the operating system vendor does not offer anything else. NFS exacerbates all of the above problems. Some NFS implementations don't provide any reliable locking mechanism. With mbox and mh formats, if two machines deliver mail to the same user, or if a user reads mail anywhere except the delivery machine, the user's mail is at risk. maildir works without trouble over NFS.