The backup job on my SharePoint 2007 (server A) fails since the job running under local NETWORK SERVICE account tries to access a remote share(Server B) to store backup files. Adding Server A' computer account(domain\ServerA$) to the Server B's folder permission solves the problem. But are there any security issues that I'm not aware of? Would you recommend this approach?
Any process running on that computer that is running as, or can assume, the Network Service account can access the folder with the permission set in the ACE.
The security risk will depend entirely on who can access that computer and what level of permissions they have. If it's an XP machine where Domain Users has been added to the Local Administrators group, then any domain user can potentially impersonate the Network Service account and gain access. If it's a locked down server with good Anti-Malware and extremely limited access, then it's pretty secure.