Splitting the command into two like this:
jhead -mkexif Narsaaq.jpg
jhead -ts1992:09:05-13:00:00 -ft Narsaaq.jpg 

seems to work (does not crash), but valgrind still reports memory error(s):

$ valgrind --leak-check=full --show-reachable=yes jhead -mkexif Narsaaq.jpg 
==23119== Memcheck, a memory error detector.
==23119== Copyright (C) 2002-2008, and GNU GPL'd, by Julian Seward et al.
==23119== Using LibVEX rev 1884, a library for dynamic binary translation.
==23119== Copyright (C) 2004-2008, and GNU GPL'd, by OpenWorks LLP.
==23119== Using valgrind-3.4.1-Debian, a dynamic binary instrumentation framework.
==23119== Copyright (C) 2000-2008, and GNU GPL'd, by Julian Seward et al.
==23119== For more details, rerun with: -v
==23119== 
==23119== Invalid read of size 1
==23119==    at 0x408955: (within /usr/bin/jhead)
==23119==    by 0x40890A: (within /usr/bin/jhead)
==23119==    by 0x408BE2: (within /usr/bin/jhead)
==23119==    by 0x405E22: (within /usr/bin/jhead)
==23119==    by 0x405F0A: (within /usr/bin/jhead)
==23119==    by 0x4020A2: (within /usr/bin/jhead)
==23119==    by 0x403F25: (within /usr/bin/jhead)
==23119==    by 0x50CF5A5: (below main) (in /lib/libc-2.9.so)
==23119==  Address 0x54233f8 is 0 bytes after a block of size 160 alloc'd
==23119==    at 0x4C278AE: malloc (vg_replace_malloc.c:207)
==23119==    by 0x405B0B: (within /usr/bin/jhead)
==23119==    by 0x405F0A: (within /usr/bin/jhead)
==23119==    by 0x4020A2: (within /usr/bin/jhead)
==23119==    by 0x403F25: (within /usr/bin/jhead)
==23119==    by 0x50CF5A5: (below main) (in /lib/libc-2.9.so)
==23119== 
==23119== Invalid read of size 1
==23119==    at 0x40896C: (within /usr/bin/jhead)
==23119==    by 0x40890A: (within /usr/bin/jhead)
==23119==    by 0x408BE2: (within /usr/bin/jhead)
==23119==    by 0x405E22: (within /usr/bin/jhead)
==23119==    by 0x405F0A: (within /usr/bin/jhead)
==23119==    by 0x4020A2: (within /usr/bin/jhead)
==23119==    by 0x403F25: (within /usr/bin/jhead)
==23119==    by 0x50CF5A5: (below main) (in /lib/libc-2.9.so)
==23119==  Address 0x54233f9 is 1 bytes after a block of size 160 alloc'd
==23119==    at 0x4C278AE: malloc (vg_replace_malloc.c:207)
==23119==    by 0x405B0B: (within /usr/bin/jhead)
==23119==    by 0x405F0A: (within /usr/bin/jhead)
==23119==    by 0x4020A2: (within /usr/bin/jhead)
==23119==    by 0x403F25: (within /usr/bin/jhead)
==23119==    by 0x50CF5A5: (below main) (in /lib/libc-2.9.so)
Modified: Narsaaq.jpg
==23119== 
==23119== ERROR SUMMARY: 2 errors from 2 contexts (suppressed: 8 from 1)
==23119== malloc/free: in use at exit: 240 bytes in 1 blocks.
==23119== malloc/free: 21 allocs, 20 frees, 68,789 bytes allocated.
==23119== For counts of detected errors, rerun with: -v
==23119== searching for pointers to 1 not-freed blocks.
==23119== checked 81,504 bytes.
==23119== 
==23119== 
==23119== 240 bytes in 1 blocks are still reachable in loss record 1 of 1
==23119==    at 0x4C279E1: realloc (vg_replace_malloc.c:429)
==23119==    by 0x405BD3: (within /usr/bin/jhead)
==23119==    by 0x405F0A: (within /usr/bin/jhead)
==23119==    by 0x4020A2: (within /usr/bin/jhead)
==23119==    by 0x403F25: (within /usr/bin/jhead)
==23119==    by 0x50CF5A5: (below main) (in /lib/libc-2.9.so)
==23119== 
==23119== LEAK SUMMARY:
==23119==    definitely lost: 0 bytes in 0 blocks.
==23119==      possibly lost: 0 bytes in 0 blocks.
==23119==    still reachable: 240 bytes in 1 blocks.
==23119==         suppressed: 0 bytes in 0 blocks.