As I ended my last post, I found some errors in my Database Maintenance Plan. Checking the errors produced a commonality; the database must be in single user mode. Apparently the processes attempt to put the databases in single user mode when they try to do a repair. If the databases are in use at the time, it won't be able to do so and an error results. Checking with my good buddy Mr. Google, I found Microsoft article 290622 which explained the issue. I have now set the Database Maintenance Plan to not Attempt to repair any minor problems found during the Integrity Checking process.
Having made the changes I then re-ran each previously failed job. To do so, I went to Management/SQL Server Agent/Jobs, right clicked on each failed job in turn, and selected Start Job. I then highlighted 'Job' again in the Navigation Pane and clicked on the refresh button every so often to see that the job was executing and when it finished. Now I have all blue in my jobs listing.