I got a complaint from a client that when a checkout error appeared on their site, the screen would scroll down so that the error notice was only visible for a fraction of a second before scrolling up where it disappeared off screen or under the sticky site header. It is WooCommerce default behaviour to scroll to the top of the checkout form after an errored checkout submit, but depending on your theme’s template for this page and not to mention your screen size, it could definitely cause confusion.

As it is usually the quickest path to applying a fix for a situation like this; I googled “woocommerce prevent scroll to checkout error”. Nothing useful…
The next step was to open checkout.js which is one of the native WC assets that would be most likely to contain the scrolling code. Fortunately it did. It has some jQuery telling the screen to animate to the top of $( 'form.checkout' ) over the course of 1 second. The bad part is that instead of replacing the entire checkout.js there’s not really a way to remove these 3 lines of code. The good part is that right after this scrolling trigger it fires an event on the body tag! Namely “checkout_error”. So what I ended up doing is to listen to the checkout_error event trigger and stop scrolling right away. This means it will stop before it event starts, so you don’t see any scrolling:

jQuery( document.body ).on( 'checkout_error', function() {
	jQuery( 'html, body' ).stop();
} );

Update 9 Sep 2018 (contributed via comments)

If the checkout_error event doesn’t fire for some reason, you could also prevent scrolling after every ajax request like so:

jQuery( document ).ajaxComplete( function() {
	if ( jQuery( 'body' ).hasClass( 'woocommerce-checkout' ) || jQuery( 'body' ).hasClass( 'woocommerce-cart' ) ) {
		jQuery( 'html, body' ).stop();
	}
} );