> How do we spot any ASAN issues, though? Does ASAN change the process' return code on errors?

It aborts:
$ cat /tmp/test.c
int main(int argc, char *argv[])
{
    int bar[16] = {0};

    /* oops */
    return bar[16];
}
$ gcc -Wall -fsanitize=address -o /tmp/test /tmp/test.c
$ /tmp/test
=================================================================
==15028== ERROR: AddressSanitizer: stack-buffer-overflow on address
0xbffab500 at pc 0x80485ec bp 0xbffab488 sp 0xbffab47c
READ of size 4 at 0xbffab500 thread T0
    #0 0x80485eb (/tmp/test+0x80485eb)
    #1 0xb5fd8a62 (/lib/i386-linux-gnu/i686/cmov/libc-2.18.so+0x19a62)
    #2 0x8048490 (/tmp/test+0x8048490)
Address 0xbffab500 is located at offset 96 in frame <main> of T0's stack:
  This frame has 1 object(s):
    [32, 96) 'bar'
HINT: this may be a false positive if your program uses some custom
stack unwind mechanism or swapcontext
      (longjmp and C++ exceptions *are* supported)
Shadow bytes around the buggy address:
  0x37ff5650: 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
  0x37ff5660: 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
  0x37ff5670: 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
  0x37ff5680: 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
  0x37ff5690: 00 00 00 00 f1 f1 f1 f1 00 00 00 00 00 00 00 00
=>0x37ff56a0:[f3]f3 f3 f3 00 00 00 00 00 00 00 00 00 00 00 00
  0x37ff56b0: 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
  0x37ff56c0: 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
  0x37ff56d0: 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
  0x37ff56e0: 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
  0x37ff56f0: 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
Shadow byte legend (one shadow byte represents 8 application bytes):
  Addressable:           00
  Partially addressable: 01 02 03 04 05 06 07
  Heap left redzone:     fa
  Heap righ redzone:     fb
  Freed Heap region:     fd
  Stack left redzone:    f1
  Stack mid redzone:     f2
  Stack right redzone:   f3
  Stack partial redzone: f4
  Stack after return:    f5
  Stack use after scope: f8
  Global redzone:        f9
  Global init order:     f6
  Poisoned by user:      f7
  ASan internal:         fe
==15028== ABORTING

You obviously don't see here, but it also colors the output in a terminal :-)