Red shift is definate fact. There is no disputing it's effects. However, as they say, it is not the most reliable method for measuring the distance of a galaxy.
You can measure a galaxy's distance away using Hubbles law: v = H*d (V= velocity, H= Hubble's constant and d=distance). Ie You can work out distance as it is proportional by Hubble's constant to a galaxies velocity away from us. You work out the velocity away using the Doppler shift as described above. The wavelength of the radiation emitted, say, from a Hydrogen atom comes in definate quanta. Thus by comparing the new wavelength to the old through this equation:
((W-Wo)/Wo)*C = V
(W = new wavelength, Wo = wavelength when not moving as measured on earth, C = speed of light, V = velocity). I would type lamda but I don't have that key on my keyboard .
Thus you have the velocity away from us. Note, that Hubble's constant is still disputed today and not truly known. Also, if the galaxy is accelerating or decelerating (possibly due to a collision or so forth) then yes it becomes less accurate.
For Cepheid Variable Stars (stars that pulse light), using the stars apparent luminosity, and its absolute luminity, and comparing the two, you can work out the distance away. You do this as from the Period of the pulse, you can work out Absolute Luminosity (M). Apparent Luminosity (m) is simply relative birghtness how it appears and then using d = 10^((5 - M + m)/5) you have the distance in parsecs. This process was discovered by Henrietta Levitt.
Also, not that once you have worked out Hubble's constant in the first method by measuring the gradient when plotting Distance versus Velocity, using H = 1/T (T = Age of Universe) you can work out the age of the Universe.
Hope this helps. Also, <3 Physics.
Source = a course at Cambridge University.