I have had a few crashes since last post. This time I succeeded to record the debug print outs from the modem-manager. Since I have not had any crashes when running with the WLAN, I thought it could be interesting to see if the 3G connection could be the problem. Below is the log.

** (modem-manager:1969): DEBUG: (ttyACM0): probe requested by plugin 'Generic'
** (modem-manager:1969): DEBUG: (ttyACM1): probe requested by plugin 'Generic'
** (modem-manager:1969): DEBUG: (ttyACM2): probe requested by plugin 'Generic'
** (modem-manager:1969): DEBUG: (ttyACM3): probe requested by plugin 'Generic'
** (modem-manager:1969): DEBUG: (ttyACM0): --> 'AT+GCAP<CR>'
** (modem-manager:1969): DEBUG: (ttyACM0): <-- 'AT+GCAP<CR><CR><LF>+GCAP: +CGSM, +DS<CR><LF><CR><LF>OK<CR><LF>'
** (modem-manager:1969): DEBUG: (ttyACM1): --> 'AT+GCAP<CR>'
** (modem-manager:1969): DEBUG: (ttyACM2): --> 'AT+GCAP<CR>'
** (modem-manager:1969): DEBUG: (ttyACM3): --> 'AT+GCAP<CR>'
** (modem-manager:1969): DEBUG: (ttyACM1): <-- 'AT+GCAP<CR><CR><LF>+GCAP: +CGSM, +DS<CR><LF><CR><LF>OK<CR><LF>'
** (modem-manager:1969): DEBUG: Added modem /sys/devices/pci0000:00/0000:00:1d.7/usb1/1-4
** (modem-manager:1969): DEBUG: Exported modem /sys/devices/pci0000:00/0000:00:1d.7/usb1/1-4 as /org/freedesktop/ModemManager/Modems/0
** (modem-manager:1969): DEBUG: (ttyACM2): --> 'AT+GCAP<CR>'
** (modem-manager:1969): DEBUG: (ttyACM3): --> 'AT+GCAP<CR>'
** (modem-manager:1969): DEBUG: (ttyACM2): --> 'AT+GCAP<CR>'
** (modem-manager:1969): DEBUG: (ttyACM3): --> 'AT+GCAP<CR>'
** (modem-manager:1969): DEBUG: (ttyACM3): --> 'ATI<CR>'
** (modem-manager:1969): DEBUG: (ttyACM3): --> 'AT+CPIN?<CR>'
** (modem-manager:1969): DEBUG: (ttyACM3): --> 'AT+CGMM<CR>'
** (modem-manager:1969): DEBUG: (ttyACM0): --> 'ATZ E0 V1 +CMEE=1<CR>'
** (modem-manager:1969): DEBUG: (ttyACM0): <-- 'ATZ E0 V1 +CMEE='
** (modem-manager:1969): DEBUG: (ttyACM0): <-- '1<CR>'
** (modem-manager:1969): DEBUG: (ttyACM0): <-- '<CR><LF>OK<CR><LF>'
** (modem-manager:1969): DEBUG: (ttyACM0): --> 'ATE0 +CMEE=1<CR>'
** (modem-manager:1969): DEBUG: (ttyACM0): <-- '<CR><LF>OK<CR><LF>'
** (modem-manager:1969): DEBUG: (ttyACM0): --> 'ATX4 &C1<CR>'
** (modem-manager:1969): DEBUG: (ttyACM0): <-- '<CR><LF>OK<CR><LF>'
** (modem-manager:1969): DEBUG: (ttyACM0): --> 'AT+CREG=0<CR>'
** (modem-manager:1969): DEBUG: (ttyACM0): <-- '<CR><LF>OK<CR><LF>'
** (modem-manager:1969): DEBUG: (ttyACM0): --> 'AT+CFUN=1<CR>'
** (modem-manager:1969): DEBUG: (ttyACM0): <-- '<CR><LF>OK<CR><LF>'
** (modem-manager:1969): DEBUG: (ttyACM0): --> 'AT+CPIN?<CR>'
** (modem-manager:1969): DEBUG: (ttyACM0): <-- '<CR><LF>+CPIN: READY<CR><LF>'
** (modem-manager:1969): DEBUG: (ttyACM0): <-- '<CR><LF>OK<CR><LF>'
** (modem-manager:1969): DEBUG: (ttyACM0): --> 'AT+COPS=0,,<CR>'
** (modem-manager:1969): DEBUG: (ttyACM0): <-- '<CR><LF>OK<CR><LF>'
** (modem-manager:1969): DEBUG: (ttyACM0): --> 'AT+CREG?<CR>'
** (modem-manager:1969): DEBUG: (ttyACM0): <-- '<CR><LF>+CREG: 0,1<CR><LF>'
** (modem-manager:1969): DEBUG: (ttyACM0): <-- '<CR><LF>OK<CR><LF>'
** (modem-manager:1969): DEBUG: Registration state changed: 1
** (modem-manager:1969): DEBUG: (ttyACM0): --> 'AT+COPS=3,2;+COPS?<CR>'
** (modem-manager:1969): DEBUG: (ttyACM0): <-- '<CR><LF>+COPS: 0,2,"24008",2 <CR><LF><CR><LF>OK<CR><LF>'
** (modem-manager:1969): DEBUG: (ttyACM0): --> 'AT+COPS=3,0;+COPS?<CR>'
** (modem-manager:1969): DEBUG: (ttyACM0): <-- '<CR><LF>+COPS: 0,0,"Telenor SE",2 <CR><LF><CR><LF>OK<CR><LF>'
** (modem-manager:1969): DEBUG: (ttyACM0): --> 'AT+CSQ<CR>'
** (modem-manager:1969): DEBUG: (ttyACM0): <-- '<CR><LF>+CSQ: 99,99<CR><LF><CR><LF>OK<CR><LF>'
** (modem-manager:1969): DEBUG: (ttyACM0): --> 'AT+CGDCONT?<CR>'
** (modem-manager:1969): DEBUG: (ttyACM0): <-- '<CR><LF>+CGDCONT: 1,"IP","services.telenor.se","0.0.0.0",0,0<CR><LF>'
** (modem-manager:1969): DEBUG: (ttyACM0): <-- '+CGDCONT: 2,"IP","services.telenor.se","0.0.0.0",0,0<CR><LF>'
** (modem-manager:1969): DEBUG: (ttyACM0): <-- '+CGDCONT: 3,"IP","services.telenor.se","0.0.0.0",0,0<CR><LF>'
** (modem-manager:1969): DEBUG: (ttyACM0): <-- '+CGDCONT: 4,"IP","services.telenor.se","0.0.0.0",0,0<CR><LF>'
** (modem-manager:1969): DEBUG: (ttyACM0): <-- '+CGDCONT: 5,"IP","internet.telenor.se","0.0.0.0",0,0<CR><LF>'
** (modem-manager:1969): DEBUG: (ttyACM0): <-- '<CR><LF>OK<CR><LF>'
** (modem-manager:1969): DEBUG: (ttyACM0): --> 'ATD*99***5#<CR>'
** (modem-manager:1969): DEBUG: (ttyACM0): <-- '~\-1}#\-64!}!}!} }9}#}%\-62#}%}(}"}'}"}"}&} } } } }%}&\-113\-123\-43+;\-115~'
** (modem-manager:1969): DEBUG: (ttyACM0): <-- '<CR><LF>CONNECT<CR><LF>'

Some other comments:
When the last crash occurred, during which above modem-manager debug log is taken, the CPU load was close to hundred percent when I was running Firefox. There seems to be a problem with Firefox but heavy CPU load should not crash the system.