On our system, log.aad4225 has never been purged and the output to the file is not dated.

I'm considering emptying the log file just prior to executing Reorganize Tables so that when I look at the log, I'll know that the output is from the most recent execution.

Is there a problem emptying the existing log and saving it's contents elsewhere?

There is no problem in moving the log file elsewhere. When u need to see the info regarding earlier re-org , u need to see info in the original file.