What are the disadvantages of a Tail providing lift? (tandem-wings included)
A lifting tail just means lower static stability.

You are correct, flying in the downwash of the wing makes the tail less efficient. But that does not mean it is all bad: Since downwash increases with lift coefficient, the tail effectively sees a smaller angle of attack variation than the wing, so it maintains a healthy margin from stalling even while the wing is stalled. This helps to keep the aircraft controllable well into a stall (within limits, of course). 

The reduction in downwash as the center wing stalls will even add a positive AoA gradient during the incipient stall which adds some more stability, making it harder for the pilot to command a further AoA increase.

And performance-wise, the download on the tail in conjunction with downwash actually might create a bit of thrust on the tail.

Concerning Rutan Designs: Their different looks are not for better performance but merely the expression of an oversized ego and his way of self-promotion.



EDIT:

The many downvotes I now collect for speaking my mind freely shows how well the self-promotion of Burt Rutan works. But it cannot bend the laws of physics which guide my opinion. Which I will continue to express freely.