Life changing. Thank you.

That wasn't a boom mic. Everyone knows at that point in time, the enterprise D was going through a particularly bad infestation of Candelibrian Ceiling Rats. They had to call Q to exterminate them. Originally they tried using that green beam thing, but stupid Picard got stuck on the ship and almost got bumped off by it, so they had to take the machine out of service to install better safety interlocks. I hear they used the same company that installs the safety protocols on the holodeck.

He even calls Picard 'Patrick'

My favorite Next Gen blooper is in the episode where Tasha Yar's daughter shows up as a Romulan officer. You can see a technician's face clearly reflected in a glass sculpture. It's only visible for a split second, but I noticed it when the episode first aired, and wondered at the time whether it was Gene Roddenberry's face inserted as a tribute. That actually would have been a cool thing to do.

Yes. Sometimes the boom mike makes it into the shot. During the days these episodes were made, televisions has what was called the "overscan" area of the screen or that part of the screen that was hidden. It appears this mike might have been in that area of the screen so the editors may not have noticed it. With today's plasma screen HD TVs, you are seeing the entire screen, so producers have to be more careful.

this is when Picard becomes Heisenberg

Two I've noticed before.  In the first season episode "Too Short a Season" after speaking to the Admiral on the viewscreen, Picard goes to the turbolift to meet the him in the transporter room.  If you look closely as Picard approaches the turbolift door you can see him make a funny face to someone off camera.  And on Star Trek Enterprise, on the episode where Shran fights Archer, when the shiny ice cutter weapons are behind held you can see reflections of plywood and 2x4 boards off-camera on the set.  Quite funny. :-)

There's a scene in Beetlejuice where virtually the whole thing's visible for about fifteen seconds.

Funniest Trek blooper of all: in episode "Unification II" (TNG, season 5, episode 8), just after Data applies the Vulcan Nerve Pinch to Sela and he and Picard and Spock escape from her office, the camera pans across and on her desk is a reflective, pyramid-shaped object. Play it back slowly and you'll find the face of a man wearing glasses and CHEWING BUBBLE GUM reflected in it!!

I found a boom mic in the episode I'm currently viewing, did a Google search which led me here.

So focused on the characters I did not even noticed the

There's one where Patrick gestures to a corner of the room for seemingly no reason, he appears to shoosh someone as if to not alert the other person in the room.

There's one more, in 9th degree when Barclay disagrees in the meeting and stands up to show how to program new matrix to fix the array, and you can see Patrick Stewart gets out of character and starts chewing gum

There are several moments like this. It has to do with the camera aspect ratio and the version you are watching. On the DVD, you can see a hand take Mistress Biata 's wine glass when after Cmdr. Riker hands her the glowy crystal IN BED (I think the episode is Angel One).

There are more boom mic slip ups than this in TNG. Keep your eyes peeled!

the tribble did it. everyone knows that.