Galaxy S3 Error/Crash Log Location
logcat might give you some information but that is cleared when the device reboots. 

abd logcat will connect you to the "rolling log". 

logcat is not stored in a file, only in a memory stream but you can easily dump it to file.

adb logcat -d -v time > logfile.txt

using the options I listed above will give you a time stamp of when events occur. The -d indicates you are dumping to a file, do not "block". -v time formats the log with event times. 

Instead of &gt; logfile.txt you could do -f /path/to/logfile.txt.