And the "checksum" errors are, typically, created if you access a repository file between the time that the checksum information has been changed and the actual file contents have been changed. When a repository is updated, the checksum file is first changed, and then the individual files are replaced by the newer ones. Thus attempting to access a file that is in the process of being replaced will produce a "checksum" error, but access to other, unchanged, files will not cause an error.
Usually, waiting an hour or so will give the repositories time to finish the update, and your YUM session should, once again, work without any problem.
(Of course, you can also get a checksum error if your connection is flaky, but that usually causes other problems that are obvious.)