How can I fully log all bash scripts actions?

I generally put something similar to the following at the beginning of every script (especially if it’ll run as a daemon):

#!/bin/bash
exec 3>&1 4>&2
trap 'exec 2>&4 1>&3' 0 1 2 3
exec 1>log.out 2>&1
# Everything below will go to the file 'log.out':

Explanation:

1. exec 3>&1 4>&2

   Saves file descriptors so they can be restored to whatever they were before redirection or used themselves to output to whatever they were before the following redirect.

2. trap 'exec 2>&4 1>&3' 0 1 2 3

   Restore file descriptors for particular signals. Not generally necessary since they should be restored when the sub-shell exits.

3. exec 1>log.out 2>&1

   Redirect stdout to file log.out then redirect stderr to stdout. Note that the order is important when you want them going to the same file. stdout must be redirected before stderr is redirected to stdout.

From then on, to see output on the console (maybe), you can simply redirect to &3. For example,

echo "$(date) : part 1 - start" >&3

will go to wherever stdout was directed, presumably the console, prior to executing line 3 above.