Redirecting stdout+stderr such that both get written to a file while still outputting to stdout is simple enough:
cmd 2>&1 | tee output_file
>
Here's how I do it:
exec 3>log ; example_command 2>&1 1>&3 | tee -a log ; exec 3>&-
bash$ exec 3>log ; { echo stdout ; echo stderr >&2 ; } 2>&1 1>&3 | \
tee -a log ; exec 3>&-
stderr
bash$ cat log
stdout
stderr
Here's how that works:
exec 3>log sets up file descriptor 3 to redirect into the file called log, until further notice.
example_command to make this a working example, I used { echo stdout ; echo stderr >&2 ; }. Or you could use ls /tmp doesnotexist to provide output instead.
Need to jump ahead to the pipe | at this point because bash does it first. The pipe sets up a pipe and redirects the file descriptor 1 into this pipe. So now, STDOUT is going into the pipe.
Now we can go back to where we were next in our left-to-right interpretation: 2>&1 this says errors from the program are to go to where STDOUT currently points, i.e. into the pipe we just set up.
1>&3 means STDOUT is redirected into file descriptor 3, which we earlier set up to output to the log file. So STDOUT from the command just goes into the log file, not to the terminal's STDOUT.
tee -a log takes it's input from the pipe (which you'll remember is now the errors from the command), and outputs it to STDOUT and also appends it to the log file.
exec 3>&- closes the file descriptor 3.