styling back end widget form and enabling multi widget feature

I don’t know if the tutorial uses any deprecated function, you can check that enabling WP_DEBUG in your wp-config.php.

Anyway, by the time it was written the new Widgets API didn’t exist.

The Codex is your friend, read the Codex:
http://codex.wordpress.org/Widgets_API

And for styling the widgets admin area refer to this post:
Highlight custom widgets in the admin area?

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