Complex three-dimensional patterns of multifunctional optical traps can be encoded in phase-only computer-generated holograms and projected with the holographic optical trapping technique. The trap-forming holograms, in turn, are implemented as diffractive optical elements whose phase transfer functions generally do not faithfully reproduce the design. We demonstrate that phase encoding errors reduce the overall intensities of the projected traps but, remarkably, do not affect their positions, relative intensities or mode structure. We exploit this robust performance to implement dual-color holographic optical tweezers with a single hologram.