That first one is unfortunate because I cannot read all of the error message. Plus it appears as if it isn't the usual error dialog, which means it probably didn't file an error report.
As for the "out of memory" issue: I'm clueless. I have no idea how this could happen, and doubt there's anything the application could do differently to prevent it. My only suggestion is to make sure you're using Auto Save WITH the backup option, and if you see this error, save the tournament, exit the TD and restart it.
How big is your player database, by the way?
I have tested this in the past with a DB of over 5000 players. And that was in the days of slower PCs, less memory, and a much less robust Internet Explorer.