Yes, it is important! It affects:
1. Loading/displaying speed
2. Displaying in different browsers
3. SEO promoting
Check if your site has any errors here: https://validator.w3.org/nu/
This resource shows only HTML errors in the code.
If you have JS, CSS, PHP, and other errors, then I will post a separate Kwork.
Look at the last error. If there is a "Fatal Error" inscription, then the site has more errors, but after this one, it is not possible to count all the other errors.
If you fix errors on the main page, there will be fewer errors on other pages. For full fixing, you need to edit all pages of the site.
If you fix errors on one product, probably, errors on other products will be gone, because they are sharing one pattern.
Sometimes (but rarely) fixing an error can start a big chain of edits. Usually, it is related to ... actually, you don't need to dive into the nuances. If I don't fix an error, I will give you a full description of why I had to leave it.
If errors are in the engine or plugin code, after updating them, errors will come back. I don't recommend updating, but if it is necessary, then you will need to ask developers who make these errors to fix them.