This is not a new issue, it has been rarely and randomly affecting upgrades for a long time. I have looked into this several times and never found a pattern of why some sites have problems and others do not. I have never been able to reproduce this on demand. Before every release there are dozens of different upgrades tested, 5.6.2 was no exception.
The telerik failure is usually caused by a failure to update the web.config file.
To fix this:
Verify the Telerik.Web.UI.dll version from the website bin directory.
Go to root directory of the website
Expand Bin folder
Right click Telerik.Web.UI.dll and select properties
Click the details Tab, Product Version should be 2010.03.1317.35
If the .dll is not the correct version, you can get the latest from:
\Install\Module\Telerik_05.06.02_Install.zip\bin\ in the upgrade.zip
\bin in the install.zip
In Web.config, look for
<assemblyIdentity name="Telerik.Web.UI" publicKeyToken="121fae78165ba3d4" />
<bindingRedirect oldVersion="2008.0.0.0-2020.0.0.0" newVersion="2010.03.1317.35" />
Ensure that the Web.config has the newVersion set to the same as the .dll in your bin directory. Be aware that there will likely be several commented out bindingRedirect entries, the only one that counts is the one that is NOT commented out.
Finally to address the .Net version question. Basically MS made a confusing mess of the numbering system. Here is a blog
that helps in understanding the situation.
A quick summary of the version relevant to this conversation.
There are only two current run times, 2.0 and 4.0. You can choose one of those for each site in IIS.
3.0, and 3.5 are just extra libraries that run on the 2.0 run time. If they are installed they are always available to a 2.0 run time. Current versions of DotNetNuke require 3.5.
4.0 is a new runtime and new libraries that include everything that came before. One server can have both 4.0 and 2.0 installed with some sites running on each.