How to perform Nameserver cleanup after transferring domains

Hi, I have transferred some accounts from another cpanel server using transfer tool. When i check in DNS zone manager, it shows old server's Nameservers, i have already changed domain's Nameservers and it is resolving to new server. How do i properly change it in "DNS zone manager". Should i also change the serial in DNS if i make changes. Is it OK to leave them? Also, Mname is set to Old server. Rname is same email ID in both servers.