Low cost power supply redundancy
1) Is there any problem inherently with this design? - To maintain optimal cross regulation, the feedback voltage reference for the SMPS control loop is derived generally from one or more secondary outputs which have the lowest voltage/s and the highest power drawn. Having said this, your scheme could work well if the load connected to the output rails are 'not' voltage sensitive and can tolerate the series diode drops (in your suggested scheme, one diode drop per rail irrespective of the diodes selected). Adding Schottky diodes (or similar low Vf Diodes) could likely affect the circuitry powered; especially on the 3.3V rail. Note that the forward voltage of Schottky diodes increase with higher currents drawn. Since your application is meant as a 'back-up' (i.e. Output load is within the power rating of a single Power supply), you needn't ensure that voltages on each of the regulated outputs (especially on the high current rails) being diode-'OR-ed' are closely matched.

2) "Forward voltage per leg" as 1.2V - This implies that while drawing 25A through each diode instantaneously, this single diode would drop an absolute maximum of 1.2VDC; as per your proposed scheme of using 2 of 4 diodes in each Bridge.