We measure the noise added by an atomic point contact operated as a displacement detector. With a microwave technique, we increase the measurement speed of atomic point contacts by a factor of 500. The measurement is then fast enough to detect the resonant motion of a nanomechanical beam at frequencies up to 60 MHz and sensitive enough to observe the random thermal motion of the beam at 250 mK. We demonstrate a shot-noise limited imprecision of 2.3 fm/square root[Hz] and observe a 78 aN/square root[Hz] backaction force, yielding a total uncertainty in the beam's displacement that is 42 times the standard-quantum limit.