bashzsh
I am using 'zsh' by default.
But when I am in my zsh shell, I enter 'bash' to switch to bash, why the $SHELL variable does not change?
Can I make screen to use whatever shell I right before execute the 'screen' command?
zsh % screen
<the shell is zsh>
zsh % bash
bash $ screen
<the shell is still bash, can I make screen to automatically start bash here>
The symptoms you describe are a lot like the bugs http://pad.lv/360253 and http://pad.lv/625192 so I suggest you add some debugging information to the latter. See https://wiki.ubuntu.com/Apport for how to get a crash file to attach to the bug.
As an aside, how can I make zsh the default terminal?
It's a shell, not a terminal. But to change it just for your account, you want
chsh -s /bin/sh
and to change it for newly-added accounts, change DSHELL in /etc/adduser.conf.
This feature is provided by the command-not-found 
package. Ubuntu installs it by default, and makes it active by default in bash but not in zsh. Just add this line to your ~/.zshrc:
. /etc/zsh_command_not_found
Best Answer
The SHELL variable (along with some other variables, such as HOME and USER) is set by the process that logs you in. It is set to the login shell value set in the passwd database (/etc/passwd). It is not meant to reflect the shell you're currently using.
screen uses the SHELL variable to determine what shell to run inside the screen, so you can override that by running e.g.
And if you want bash to be your login shell instead of zsh, you can run the
chsh(change shell) command as your user.