After many attempts I have finally got my system working using Maverick Server and clients. In case it's of any help I have summarised what I did below.
I had all the normal problems post upgrade from ML, network users not being able to login, unable to change passwords, open directory issues etc.
The solution as others have said is DNS DNS DNS DNS!!!
I bought a copy of OS X Server Essentials 10.9, the one that's used on the three day Apple course and started from page 1; I also watched Todd Olthoff on Youtube, thanks Todd! The rest is as follows:
Setup AirPort Extreme with DHCP, IP range 10.0.0.x, DNS on the internet tab set to service provider external DNS servers (or Google etc)
Clean install of Mavericks on the server followed by updates
Turn wifi off on server and hardwire to AirPort Extreme
Create Local Admin account give admin privileges and set time zone
Rename the startup volume as ‘Server’
Turn on remote management
Change the Computer Name in sharing to ‘server’
On the server, in System Preferences, Network, change DHCP to manual, IP 10.0.0.2 subnet 255.255.255.0 Router 10.0.0.1 Advanced DNS tab, delete all and enter 10.0.0.1 ie the Airport Extreme. Search Domains to your domain, ie example.com and click apply.
Install server from the App store
When complete open Server Admin and change the Computer name to ‘server’ and host Name to server.example.com also click edit and ensure the networks setting have been retained. Say yes to setup DNS.
Open system prefs and network, go advanced and DNS. Change the DNS from 10.0.0.1 to 127.0.0.1 and make sure the Search Domain is still example.com.
Open network utility and Lookup 10.0.0.2 and you should get server.example.com and do it the the other way round to get 10.0.0.2
Turn on file sharing and websites and open directory to create the master with ‘diradmin’ and password.
Create network user accounts
Start mail, entering example.com in the provide mail box
On the client computer, clean install Mavericks
On client manually change the network settings to a fixed IP 10.0.0.100 and set the DNS to the server only, 10.0.0.2.
I then tried to bind a client to the server and great it worked but importantly binding server.example.com not .local
Log out and then back in, and super all users are logging in via the client computer.
The avoid manually configuring each client, back onto the airport extreme and change under Internet the first DNS to the server, 10.0.0.2 and the second to google, 8.8.8.8
back onto the client and change networks back to DHCP deleting any fixed dns entries.
Logout, login still ok, all good.
Big however, on the client away from the home network, all great, inside the network, ie at home, although access to the internet worked, login worked, no access to mail, the server website etc. Checked using Lookup and the client was unable to find www.example.com or mail.example.com, error returned, not 10.0.0.2 even though everything was good with external dns - remember it works outside the home network but was unalbe to resolve using when dns from the client is provided by the server, ie 10.0.0.2
Solution, go into Server admin, DNS and under your primary zone add machine record for www.example.com, mail.example.com with the host set to 10.0.0.2 Retain all other enties created by Mavericks.
Try again and bingo! All users logging in and out with no issues, mail running great, website up, file sharing great VPN great, the lot all working inside and outside the network.
Never an issue with ML Server but there is clearly an issue out of the box with Mavericks server as it doesn't work. Split DNS issue?
Hope this helps, but it took me with my limited knowledge of Macs a few months, as least I know a bit more now!
Les