So I took my car in to get a few gaskets replaced and came out with a huge boost leak. So I did some investigating and found the culprit. Seems like the mechanic left something out. What is suppose to connect the 2 plastic pipes to the right and below the air box?

 

I took a look at my Mini and I don't see anything missing but...the pipes are not put together correctly. It is easiest to see in your third picture. The inner pipe needs to be pushed into the outer pipe. The inner pipe has a triangular **** on it. The pipe needs to be inserted so that the *** is against the other pipe. I would say it needs to be pushed together another 3/4 - 1".

Now I'm not saying something isn't missing on the other end, at the front of the car. That's all I can see. If you can't get the pipes to go together, you may have something missing or not assembled correctly on the other end of the pipe.

 

Yea I've tried putting them together but it just doesn't line up correctly... I might just have to take it back to the shop..

 

Ok I got it to connect properly, but there is still either a boost leak or some other unexplained loss of power.

 

Being that pipe connection you're referring to in on the not-pressurized side of the intake, its definitely not your cause of loss of boost.
You need to pressure check the rest of the system and check for leaks downstream of the turbocharger compressor.

- Erik