This is part of #378 as it is now a feature included in D8 core (d.org issue):

This was something that tested really well on the D8 UX study, and we should consider adding to Backdrop as well.
User interface changes
- Form validation error messages are displayed below the respective form fields that have triggered them.
- A brief indication of the number of errors, and a link to each error is displayed in the messages area at the top of the page.
Contrib modules
Drupal 7 inline messages module

Drupal 6 (and 7) ife module

Inline Form Errors unofficial and very experimental Backdrop contrib module by @daggerhart:

~~ Advocate for this issue: @klonos ~~
Recent comments
In a blog post titled "Github Tips and Tricks for Contrib Maintainers", I'd like to see some of the following topics: When is the README sufficient for documentation? When should...
Github Tips and Tricks for Contrib Maintainers
Thanks Alejandro. That was the clues I needed.
Ubercart - Programmatically add product to cart and straight to Checkout
Have you tried uc_cart_add_item()? You need to provide the nid of the product. Then you can use backdrop_goto('cart/checkout'); to send the user to the checkout screen. uc_cart_add_item...
Ubercart - Programmatically add product to cart and straight to Checkout