I just had a chance to test ThinApp Factory 0.3.2 running with vCenter 5.1 5.1.0.5300 Build 947940 (also known as 5.1.0b), and running on vSphere 5.1.0 Build 838463. ThinApp Factory works just fine, capturing and building an application without issue.
Here's what was done in my environment so people understand the tests I did.
1. Per upgrade instructions, I upgraded vCenter 5.0 first. In my environment, I use the VMware vCenter Server Virtual Appliance. It was on 5.0 and I had to upgrade to 5.1. It should be noted, I also ran automated updates on vCenter using the default settings.
2. After upgrading vCenter (and addressing a few maintenance scenarios in my lab unrelated to this), I then upgraded one of my vSphere 5.0 servers to 5.1.0 Build 838463.
3. At the time of the upgrade, I did not have any VMs on the system.
4. After upgrading my vSphere host to 5.1.0, I then moved my ThinApp Factory instance (already using the latest from the above Flings link) to the new host under the same workpool.
NOTE: I do not have my vCenter servers in a cluster as I only have internal storage.
5. I also moved all AppFactory Workpool VMs (image and instance VMs).
6. Prior to starting ThinApp Factory, I fixed the vApp optional configuration settings to properly denote the move. See image below. Once this was resolved, I could both see existing Workpools and create new ones without the HTML 404/500 errors. I've had to force set this more than once after a move in order for proper configurations to take effect.
NOTE: The ThinApp Factory VM must be off to make these changes. It also doesn't hurt to reset your vCenter credentials (remember, don't use DOMAIN\USERNAME even if using domain credentials).
7. Once this was set, I fired things up and tested. At this point, the VMs and AppFactory did NOT have virtual hardware upgrades done nor were updated VM Tools installed. This meant NICs were failing on some.
8. I updated the VM Tools. Retesting at this point showed more network communication failures on the VMs.
9. I also shut everything down and updated the virtual hardware for the machines on each. Retesting again showed Snapshot crashes on the VMs.
10. One thing I didn't do was modify the TAF workpool to use updated network settings. But, in my case, it was easier to rebuild the Win XP Pool from scratch - which is what I did after deleting all image and instance VMs using the TAF GUI.
After rebuilding the Workpools, everything has worked fine now.
Again, the biggest issue is making sure the vApp Option Properties are set correctly with regard to Datacenter, Compute Resource, Resource Pool, Datastore and vCenter Credentials. And there are occasions where setting it multiple times and doing a couple of reboots seems to make it work better (remember, this is only a fling). 
Bottom line, TAF does work with vCenter 5.1 on vSphere 5.1.
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I should also make one other note. I've not tested earlier versions of vSphere 5.1 or vCenter 5.1 so there may well be issues which others on this thread are experiencing. Essentially, all I did was just downloaded the latest updates and tested those. 
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Hope this helps!
Message was edited by: Squidly Man