KimE: echo command simple write to given output (in this case). and result is parallels.log size = 0b.
create plain text file: ClearParallelsLog.command (make sure that extension is .command)
write following:
-------------------
#!/bin/sh
##
# clear parallels.log
##
echo > /Library/Logs/parallels.log
-----------------
and save to your Documents folder (for example)
change mode of this file:
1 - open terminal window
2 - cd to your Documents dir
3 - sudo chmod 744 ClearParallelsLog.command
4 - enter pwd
Open System Preferences > Users and Groups > Login Items "+" add created script.
logout and login and check parallels.log size (probably will have more than 0b because parallels processes is still running on background, but it is ok.)
AND: DO NOT FORGET ON IT

when you will need log from parallels.
Or, you can simple stop Parallels go to folder /Library/Logs/ delete log file empty trash and write to Parallels support about this problem (Help > Report Problem) and pray.
Because there are a lot of issue untouched more than year(s)...
definitely if Mountain Lion will require new version of Parallels, v7 will last I used.