Obligatory link to the docs.
Those are not quotes, they are backticks. MySQL allows them around table and field names work around the restriction of reserved words and special chrs. While I don't personally use them in my coding, they are a safety measure in SQLyog to make sure that it does not try and execute queries with reserved words in them. (try show table status from `mysql`; in a mysql client.. It should work.)
The ; is required and being used but it is not being echoed in the history file. Not sure why but this is not a bug. SQLyog IS putting them in where it counts, in the actual command stream. Check the log file from your mysql server. They should be there. (Mine always are)
I agree that there is a problem somewhere but these are it.
What version of mysql are you using?
Obligatory link to the docs.
The current syntax of SHOW TABLE STATUS is new in version 3.23. The previous version (SHOW STATUS `mysql`;) does work with my version of 3.23.54a. I'm not sure when it stopped working but you could be right in the fact that it's a version think.
HTH,
=C=