When run as normal user:
# ffmpeg -i elf_h264.mov -vcodec libx264 -an elf_h264.mp4 -y
ffmpeg version 1.2.1 Copyright (c) 2000-2013 the FFmpeg developers
  built on Dec 17 2013 17:20:52 with gcc 4.4.7 (GCC) 20120313 (Red Hat 4.4.7-4)
  configuration: --disable-yasm --enable-gpl --enable-version3 --enable-nonfree --enable-shared --enable-libmp3lame --enable-libx264 --enable-libfaac --enable-libtheora --enable-libvorbis --enable-libopencore-amrnb --enable-libopencore-amrwb --enable-libxvid
  libavutil      52. 18.100 / 52. 18.100
  libavcodec     54. 92.100 / 54. 92.100
  libavformat    54. 63.104 / 54. 63.104
  libavdevice    54.  3.103 / 54.  3.103
  libavfilter     3. 42.103 /  3. 42.103
  libswscale      2.  2.100 /  2.  2.100
  libswresample   0. 17.102 /  0. 17.102
  libpostproc    52.  2.100 / 52.  2.100
Input #0, mov,mp4,m4a,3gp,3g2,mj2, from 'elf_h264.mov':
  Metadata:
    major_brand     : qt
    minor_version   : 537199360
    compatible_brands: qt
    creation_time   : 2013-12-16 20:08:15
  Duration: 00:00:20.85, start: 0.000000, bitrate: 1650 kb/s
    Stream #0:0(eng): Video: h264 (Main) (avc1 / 0x31637661), yuv420p, 1920x1080, 1646 kb/s, 29.97 fps, 29.97 tbr, 2997 tbn, 5994 tbc
    Metadata:
      creation_time   : 2013-12-16 20:09:13
      handler_name    : Apple Alias Data Handler
[libx264 @ 0x969e00] using cpu capabilities: none!
Output #0, mp4, to 'elf_h264.mp4':
  Metadata:
    major_brand     : qt
    minor_version   : 537199360
    compatible_brands: qt
    Stream #0:0(eng): Video: h264, yuv420p, 1920x1080, q=-1--1, 90k tbn, 29.97 tbc
    Metadata:
      creation_time   : 2013-12-16 20:09:13
      handler_name    : Apple Alias Data Handler
Stream mapping:
  Stream #0:0 -> #0:0 (h264 -> libx264)
Error while opening encoder for output stream #0:0 - maybe incorrect parameters such as bit_rate, rate, width or height


____________________
When run as root:
# ffmpeg -i elf_h264.mov -vcodec libx264 -an elf_h264.mp4 -y -v verbose
ffmpeg version 1.2.1 Copyright (c) 2000-2013 the FFmpeg developers
  built on Dec 17 2013 17:20:52 with gcc 4.4.7 (GCC) 20120313 (Red Hat 4.4.7-4)
  configuration: --disable-yasm --enable-gpl --enable-version3 --enable-nonfree --enable-shared --enable-libmp3lame --enable-libx264 --enable-libfaac --enable-libtheora --enable-libvorbis --enable-libopencore-amrnb --enable-libopencore-amrwb --enable-libxvid
  libavutil      52. 18.100 / 52. 18.100
  libavcodec     54. 92.100 / 54. 92.100
  libavformat    54. 63.104 / 54. 63.104
  libavdevice    54.  3.103 / 54.  3.103
  libavfilter     3. 42.103 /  3. 42.103
  libswscale      2.  2.100 /  2.  2.100
  libswresample   0. 17.102 /  0. 17.102
  libpostproc    52.  2.100 / 52.  2.100
Input #0, mov,mp4,m4a,3gp,3g2,mj2, from 'elf_h264.mov':
  Metadata:
    major_brand     : qt
    minor_version   : 537199360
    compatible_brands: qt
    creation_time   : 2013-12-16 20:08:15
  Duration: 00:00:20.85, start: 0.000000, bitrate: 1650 kb/s
    Stream #0:0(eng): Video: h264 (Main) (avc1 / 0x31637661), yuv420p, 1920x1080, 1646 kb/s, 29.97 fps, 29.97 tbr, 2997 tbn, 5994 tbc
    Metadata:
      creation_time   : 2013-12-16 20:09:13
      handler_name    : Apple Alias Data Handler
[graph 0 input from stream 0:0 @ 0x8537e0] w:1920 h:1080 pixfmt:yuv420p tb:1/2997 fr:2997/100 sar:0/1 sws_param:flags=2
[libx264 @ 0x82fe80] using cpu capabilities: none!
[libx264 @ 0x82fe80] profile High, level 4.0
[libx264 @ 0x82fe80] 264 - core 138 - H.264/MPEG-4 AVC codec - Copyleft 2003-2013 - http://www.videolan.org/x264.html - options: cabac=1 ref=3 deblock=1:0:0 analyse=0x3:0x113 me=hex subme=7 psy=1 psy_rd=1.00:0.00 mixed_ref=1 me_range=16 chroma_me=1 trellis=1 8x8dct=1 cqm=0 deadzone=21,11 fast_pskip=1 chroma_qp_offset=-2 threads=12 lookahead_threads=2 sliced_threads=0 nr=0 decimate=1 interlaced=0 bluray_compat=0 constrained_intra=0 bframes=3 b_pyramid=2 b_adapt=1 b_bias=0 direct=1 weightb=1 open_gop=0 weightp=2 keyint=250 keyint_min=25 scenecut=40 intra_refresh=0 rc_lookahead=40 rc=crf mbtree=1 crf=23.0 qcomp=0.60 qpmin=0 qpmax=69 qpstep=4 ip_ratio=1.40 aq=1:1.00
Output #0, mp4, to 'elf_h264.mp4':
  Metadata:
    major_brand     : qt
    minor_version   : 537199360
    compatible_brands: qt
    encoder         : Lavf54.63.104
    Stream #0:0(eng): Video: h264 ([33][0][0][0] / 0x0021), yuv420p, 1920x1080, q=-1--1, 11988 tbn, 29.97 tbc
    Metadata:
      creation_time   : 2013-12-16 20:09:13
      handler_name    : Apple Alias Data Handler
Stream mapping:
  Stream #0:0 -> #0:0 (h264 -> libx264)
Press [q] to stop, [?] for help
[h264 @ 0xf14ca0] Increasing reorder buffer to 1
frame=   46 fps=3.9 q=-1.0 Lsize=     110kB time=00:00:01.46 bitrate= 613.6kbits/s
video:109kB audio:0kB subtitle:0 global headers:0kB muxing overhead 1.212552%
[libx264 @ 0x82fe80] frame I:1     Avg QP:15.11  size: 86734
[libx264 @ 0x82fe80] frame P:12    Avg QP:16.67  size:   914
[libx264 @ 0x82fe80] frame B:33    Avg QP:18.72  size:   389
[libx264 @ 0x82fe80] consecutive B-frames:  4.3%  0.0%  0.0% 95.7%
[libx264 @ 0x82fe80] mb I  I16..4: 60.5%  4.7% 34.8%
[libx264 @ 0x82fe80] mb P  I16..4:  0.1%  0.1%  0.0%  P16..4:  4.6%  0.2%  0.1%  0.0%  0.0%    skip:94.9%
[libx264 @ 0x82fe80] mb B  I16..4:  0.0%  0.0%  0.0%  B16..8:  2.6%  0.0%  0.0%  direct: 0.5%  skip:96.8%  L0:63.2% L1:36.8% BI: 0.1%
[libx264 @ 0x82fe80] 8x8 transform intra:5.7% inter:86.5%
[libx264 @ 0x82fe80] coded y,uvDC,uvAC intra: 62.8% 77.3% 15.6% inter: 0.1% 1.2% 0.0%
[libx264 @ 0x82fe80] i16 v,h,dc,p: 42% 18% 16% 24%
[libx264 @ 0x82fe80] i8 v,h,dc,ddl,ddr,vr,hd,vl,hu: 44% 10% 38%  3%  1%  1%  1%  1%  2%
[libx264 @ 0x82fe80] i4 v,h,dc,ddl,ddr,vr,hd,vl,hu: 35% 17% 18%  6%  5%  5%  5%  5%  4%
[libx264 @ 0x82fe80] i8c dc,h,v,p: 40% 19% 34%  7%
[libx264 @ 0x82fe80] Weighted P-Frames: Y:0.0% UV:0.0%
[libx264 @ 0x82fe80] ref P L0: 70.5%  0.2% 14.5% 14.8%
[libx264 @ 0x82fe80] ref B L0: 55.3% 37.1%  7.6%
[libx264 @ 0x82fe80] ref B L1: 98.7%  1.3%
[libx264 @ 0x82fe80] kb/s:576.14
Received signal 2: terminating.

(I interrupted the conversion once it started)