TMBTM said:

"Until this battle station is fully operation, we are vulnerable" and that was days before it's first firing on Alderaan.

Yeah, you got me, I forgot the "we are vulnerable" line!

I guess if the Death Star was all operational exept for its secret beam weapon, it would at last not be "vulnerable", indeed.

Going by the ROTJ line it's possible that the beam weapon was finished first but Tarkin didn't want to show the universe it's power until the Senate was disbanded and it couldn't open troublesome enquiries. It was odd that a design worked on before the Clone Wars and built and tested over two decades wasn't gone over with a fine toothcomb to nail down that small thermal exhaust port (imagine the conspiracy theories in the Star Wars universe).