Well done for finding the tracker issues. To explain them:
Basically, the new code in Moodle 2.3 works find if you database just contains correct data. However, if you have an old Moodle site that have been upgraded through several versions, then you tend to end up with a certain amount of garbage data in the database.
The cron code was not robust enough in the face of that old data, and two separate issues were reported. I think I done fixes for those issues yesterday, and the fixes should be reviewed and integrated into Moodle next week.
So, the simplest option is for you to wait until about Thursday or Friday next week, and then try upgrading to the latest 2.3.1+ weekly build.
The more complex option is to try to download the proposed fixes from MDL-34251 and MDL-34351, and apply them to your Moodle right now. If you did that, it would be useful testing, but you need some technical skills (mainly knowledge of git) to be able to do that.