check if you got any pole zero doublets ,if phase margin looks good in open loop gain .
but again check the common modes for input and output ,if your output common mode voltage margins so that both nmos and pmos of push pull are in saturation i.e.,s vdd-vov and vov (vov is over drive voltage vds-vgs-vt) .you input has to be with in the allowable ouput common mode voltages if you want to operate this opamp as a voltage follower .rail -rail input does not make much difference until you find voltage range common to input and output common modes.
Hope this helps !