One of our customers really seem to dislike the login url because it’s on the checkout application and it’s a bit long. I don’t believe it’s a good idea to attempt to make it prettier but does anyone know if it’s possible? Is it a case of adding the loginregister module to the shopping application and making

/login

redirect to there? Or is there a big reason why that’s a no-no? The site runs on a single domain so it’s not like there’s no SSL certificate or anything

It's possible as long as you are on SSL. That being said, i can anticipate you might find some issues along the way. I'd most likely keep the login touchpoint as is and just duplicate it. There's a fair amount of logic around navigation related to touchpoints