Optimizing Miller-Rabin Primality Test in Python
One obvious change to make is that mr_check_one(n) does a much more expensive loop than necessary. Here is a much simpler and faster version.

def mr_check_one(n):
    m = n - 1

    n = n - 1
    k =  1          
    while n % 2 == 0:  
        k += 1
        n /= 2

    return(m / 2**k) 


Also, your second function seems really broken. You allegedly loop over a, but in your first time through you redefine a, reset i and return before going through the loop more than once.