Specifically, e_ident[EI_OSABI]. The current binfmt config for most architectures requires e_ident[EI_OSABI] to be 0x00 (System V), but it is also common to have 0x03 (Linux) (and possibly others). I ran into this problem executing a container with qemu-ppc64-static. In this case, the container (the official Fedora 24 ppc64 cloud image) contained binaries with multiple stated ABIs. The qemu-ppc64-static binary supports both ABIs (I tested). I suspect the best solution is to simply mask out this byte since other ABIs might be supported as well. It appears all the mips related binfmts already do this. However, all the binfmts except for mips* have this problem.
Fixed in qemu-2.7.0-9.fc26.