I tried to fix it with:

sudo add-apt-repository ppa:jon-severinsson/ffmpeg
sudo apt-get update
sudo apt-get install ffmpeg

Still got the same crashes. Here's the new info, this time showing ffmpeg version 7:0.10.9-1~saucy1


Kernel
------
Linux razorback 3.11.0-12-generic #19-Ubuntu SMP Wed Oct 9 16:20:46 UTC 2013 x86_64 x86_64 x86_64 GNU/Linux

Architecture
------
x86_64

OS Version
------
Linux Mint 16 Petra
ffmpeg Version
------
ffmpeg version 0.10.9-7:0.10.9-1~saucy1
built on Oct 18 2013 17:40:10 with gcc 4.8.1
configuration: --arch=amd64 --disable-stripping --enable-pthreads --enable-runtime-cpudetect --extra-version='7:0.10.9-1~saucy1' --libdir=/usr/lib/x86_64-linux-gnu --prefix=/usr --enable-bzlib --enable-libdc1394 --enable-libfreetype --enable-frei0r --enable-gnutls --enable-libgsm --enable-libmp3lame --enable-librtmp --enable-libopencv --enable-libopenjpeg --enable-libpulse --enable-libschroedinger --enable-libspeex --enable-libtheora --enable-vaapi --enable-vdpau --enable-libvorbis --enable-libvpx --enable-zlib --enable-gpl --enable-postproc --enable-libcdio --enable-x11grab --enable-libx264 --shlibdir=/usr/lib/x86_64-linux-gnu --enable-shared --disable-static
libavutil      51. 35.100 / 51. 35.100
libavcodec     53. 61.100 / 53. 61.100
libavformat    53. 32.100 / 53. 32.100
libavdevice    53.  4.100 / 53.  4.100
libavfilter     2. 61.100 /  2. 61.100
libswscale      2.  1.100 /  2.  1.100
libswresample   0.  6.100 /  0.  6.100
libpostproc    52.  0.100 / 52.  0.100

openshot Version
------
openshot	1.4.3-1

ffmpeg Version
------
ffmpeg	7:0.10.9-1~saucy1

melt / mlt Version
------
No LADSPA plugins were found!

Check your LADSPA_PATH environment variable.

Version libreria MLT
------
ii  libmlt++3                                   0.8.8-2                                 amd64        MLT multimedia framework C++ wrapper (runtime)
ii  libmlt-data                                 0.8.8-2                                 all          multimedia framework (data)
ii  libmlt5                                     0.8.8-2                                 amd64        multimedia framework (runtime)

Version libreria libav
------
ii  gstreamer1.0-libav:amd64                    1.0.10-1ubuntu1                         amd64        FFmpeg plugin for GStreamer
rc  libav-tools                                 6:0.8.9-0ubuntu0.13.10.1                amd64        Multimedia player, server, encoder and transcoder
ii  libavahi-client3:amd64                      0.6.31-2ubuntu4.1                       amd64        Avahi client library
ii  libavahi-common-data:amd64                  0.6.31-2ubuntu4.1                       amd64        Avahi common data files
ii  libavahi-common3:amd64                      0.6.31-2ubuntu4.1                       amd64        Avahi common library
ii  libavahi-core7:amd64                        0.6.31-2ubuntu4.1                       amd64        Avahi's embeddable mDNS/DNS-SD library
ii  libavahi-glib1:amd64                        0.6.31-2ubuntu4.1                       amd64        Avahi GLib integration library
ii  libavc1394-0:amd64                          0.5.4-2                                 amd64        control IEEE 1394 audio/video devices
rc  libavcodec-extra-53:amd64                   6:0.8.9ubuntu0.13.10.1                  amd64        Libav codec library
ii  libavcodec53:amd64                          7:0.10.9-1~saucy1                       amd64        FFmpeg codec library
ii  libavdevice53:amd64                         7:0.10.9-1~saucy1                       amd64        FFmpeg device handling library
ii  libavfilter2:amd64                          7:0.10.9-1~saucy1                       amd64        FFmpeg video filtering library
rc  libavformat-extra-53:amd64                  6:0.8.9ubuntu0.13.10.1                  amd64        Libav file format library
ii  libavformat53:amd64                         7:0.10.9-1~saucy1                       amd64        FFmpeg file format library
ii  libavidemux0                                1:2.5.4-0ubuntu13                       amd64        a free video editor - shared libraries
rc  libavutil-extra-51:amd64                    6:0.8.9ubuntu0.13.10.1                  amd64        Libav utility library
ii  libavutil51:amd64                           7:0.10.9-1~saucy1                       amd64        FFmpeg utility library

in the screenshot attached you see my installed libavc* packets.