Okay, so when I tried to take off today I heard what sounded like air escaping from the back of the engine. Checked for coolant leaks, no leaks.
I had the windows up the first time it happened, and it sounded like air was escaping from the passenger side, as I could hear it clearly in the cabin. Almost sounded like the AC got louder on that side, or like strong wind was entering the cabin.
Second time was with the windows down. I took off, and as soon as I passed around 2.5 RPM, the noise occured again, except on the outside it sounds like a very powerful compressed air can. Did NOT sound like the turbo spooling, and it was loudest just after I let off the throttle.
During both take offs, there was a noticeable loss of boost when the sound occured.

I can't recreate this sound now since my half engine light on the tach is on, and my Mini isn't boosting properly. Not even sure where to begin looking, and I haven't seen any threads on this topic, except regarding the diverter valve.

I hope I'm being descriptive enough.

EDIT: I have 2 videos in a Google Drive folder of the sound I'm talking about here.

 

Check all the connections for the air intake system on both right and left side of the engine, IIRC I had a similar loss of power after accelerating and found that the left side intake tube next to the timing chain had popped off. That's also the area where the sound is coming from too, so maybe it's something similar. Hope this helps

 

I appreciate this. I'll check them tomorrow. Hopefully it's something as simple as that.

 

Update: It was the passenger's side charge pipe. Shop I last took it to didn't tighten it properly. Tightened it and have full boost again.
Never going to that shop again