For some reason, when I log in KDE does not start, though KDM starts just fine. I am able to get into IceWm just fine, so the issue seems to be wth KDE itself. I ran a zypper dup just to make sure I have the latest packages but this does not seem to have solved the issue.
Alternatively, can I force a re-install of KDE?
If you did just a zypper dup, that may be the cause of the issue. Assuming your Tumbleweed repo is called Tumbleweed, do
zypper dup --from Tumbleweed
Another option you have is to make sure that, in the login screen Sessions, KDE Plasma Workspace is selected.
After that messy upgrade yesterday, including KDE and upgrade/downgrades, have you tried backing up the hidden .kde4 settings file then deleting it (outside of KDE) and rebooting? KDE will then generate a new file on start up. I am going to do that for mine, even without your problem, as a precaution. 
I am back to the "Python-sip(api) issue fro Yesterday. It seems that parts of KDE 4.10 are reinstalled.
sudo zypper dup --from Tumbleweed
Loading repository data...
Warning: Repository 'openSUSE Current non-OSS updates' appears to outdated. Consider using a different mirror or server.
Reading installed packages...
Computing distribution upgrade...
9 Problems:
Problem: nothing provides python-sip(api) = 10.0 needed by python-kde4-4.11.1-3.2.i586
Problem: nothing provides python-sip(api) = 10.0 needed by python-kde4-4.11.1-3.2.x86_64
Problem: nothing provides python-sip(api) = 10.0 needed by python-kde4-4.11.1-3.2.x86_64
Problem: nothing provides python-sip(api) = 10.0 needed by python-kde4-4.11.1-3.2.x86_64
Problem: nothing provides python-sip(api) = 10.0 needed by python-kde4-4.11.1-3.2.x86_64
Problem: nothing provides python-sip(api) = 10.0 needed by python-kde4-4.11.1-3.2.x86_64
Problem: nothing provides python-sip(api) = 10.0 needed by python-kde4-4.11.1-3.2.x86_64
Problem: nothing provides python-sip(api) = 10.0 needed by python-kde4-4.11.1-3.2.x86_64
Problem: avahi-autoipd-0.6.31-2.28.x86_64 conflicts with avahi <= 0.6.31-9.2 provided by avahi-0.6.31-2.28.x86_64
Problem: nothing provides python-sip(api) = 10.0 needed by python-kde4-4.11.1-3.2.i586
Solution 1: deinstallation of python-kde4-4.10.5-1.101.3.x86_64
Solution 2: keep obsolete python-kde4-4.10.5-1.101.3.x86_64
Solution 3: break python-kde4-4.11.1-3.2.i586 by ignoring some of its dependencies
Choose from above solutions by number or skip, retry or cancel [1/2/3/s/r/c] (c): c
But now KDE is borked. So I disabled the Tumbleweed repository and am now doing a zypper dup. This SHOULD get me back to a pretty vanilla opensSUSE, right?
Did you read his other Tw thread (yesterday)? Doing that threw up a dependency problem.
Hmm, I see more package upgrades arrived today, including some KDE stuff!
PS. and no new dependency issues/solutions with this lot.
Yeah, I saw that, too.
My plan worked, BTW. I was able to get into KDE after making the install more “vanilla.” The only repositories I had enabled were the openSUSE current. (This is good, BTW, being able to revert is a really powerful troubleshooting tool!)
Then I ran sudo zypper dup --from Tumbleweed and I got the same error as yesterday. Since today my bravery is reckless, I ran sudo zypper dup and shut down my machine after-wards. Well, I was able to get back into my desktop using KDE 4.11! For some reason my login theme is Elarun. :\ not a big issue, though, I can change it later.
I will keep an eye on the status.
Yes, that problem is on the Factory mailing list now, but no real solution (nor a response from Greg K-H there yet). Interestingly one post said that Solution 4 (IIRC the one you took) was the best looking option. So my choice of Solution 2 not so good, and I see today that Kontact and its children won’t start. I’m not too bothered as I only use Tw as my test system. I’m sure that was caused by yesterday’s fiasco.
About a week back when I first installed Tw on my 12.3, I got a different login theme as zypper dup removed some branding - probably the one you call Elarun - and thought it was ok. But yesterday, choosing Solution 2, it went back to the openSUSE theme (I saw te branding packages being added) and still is after today’s update.
I changed the theme earier today and everything seems to be working.
Including the Kontact apps? If so did you take Solution 4 again for the zypper dup?
Yes, everything including Kontact works. Also, zypper dup worked fine, zypper dup --from Tumbleweed threw out an error.