Drain pipe at wrong angle. What are the consequences?
The low point is where semi-solid materials (sludge, in our vernacular) will collect and ultimately clog the sink. If your friend is willing to clean the pipe out regularly, then it's probably okay.

As you probably know, the solution is to fix the plumbing and let water run downhill.

(Edited to respond to the comment/question about possible leakage.)

I'd say that the quality of the connection and the likelihood of it leaking is a different matter. A little bit of backed up water won't create a leak. However, if the plumbing was done poorly in the first place (and it looks like it was), then it might leak. While water is running, try to gently move some of the parts and see if there's a leak. If there is, the system needs to be repaired.