SEO & Structured Data

Do you think a website with errors on structured data can still rank high on SERP? It's because I'm building site now and was thinking of removing the errors on structured data but still with no success till now. I've tried many ways to remove the errors but they're still there, up to the point that it truly makes me sick!

Now I'm thinking of forgetting about removing the errors on structured data and focusing on building back links however I still doubt if I don't remove the errors all my back link effort will be useless.

My question is:

Does anyone has a newly built site (aged less than 2 yr) which ranks high on SERP (on page 1) but still has errors on structured data?

thanks in advance

Source: SEO & Structured Data