GNU Screen makes Vim ESC key slow

Here's an actual fix. Add the following to .tmux.conf:

set -s escape-time 0

As mentioned in the comments: The server may need to be restarted.  tmux kill-server kills the server; you may need to restart it.  Alternatively, you can reload the configuration file from the command prompt inside tmux by typing your tmux prefix (default Ctrl+B) followed by : and entering source-file ~/.tmux.conf.

In its default configuration, PuTTY sends cursor keys in normal mode, e.g., ^[OA while screen sets the cursor keys to application mode, e.g., ^[[A.

That is done by screen's sending the escape sequence to turn on the keypad (in termcap ks, terminfo smkx). That happens to turn on the application mode for both the numeric keypad and the cursor keys, because both are present in the ks/smkx capability. screen uses this capability if it is present, when initializing the terminal. screen also follows up by sending the string in the termcap CS capability if it is set, hinting that the original design was to use terminal descriptions where only the keypad was initialized by ks/smkx.

You notice this difference because your key bindings expect the strings sent by the cursor keys in normal mode. If you modified the terminal description for screen to omit the part which changes the cursor keys, you could continue to use those bindings.

For instance, you could do this:

infocmp screen >foo
vi foo

and change the assignment

smkx=\E[?1h\E=,

to

smkx=\E=,

then

tic foo

to compile the modified description. If you do this as your (non-root) user, tic will put the compiled description in your ~/.terminfo directory. There are drawbacks to this approach, and using tput to obtain key-binding information is preferable. But it is simple.

Further reading:

• How do I set up a private terminfo database? (ncurses FAQ)
• Special Keys (xterm manual)