Lots of themes do have errors and although it's not ideal, in some cases it's unavoidable because of standards changing or browser differences. But those are not really the problematic kinds of errors (including the one you mention) -- they don't cause problems on the page usually. A great many of your errors are due to outdated table code -- so you could clean that up. But that also won't likely cause the problems with the responsive question.
You do have a few errors that are related to missing or open or stray tags or elements in wrong places - and those ARE relevant to layout problems.
But it's also likely that your child theme changes may be affecting how the pages resize. So you would need to look at what CSS is on the pages that work okay vs. those that do not. There is not an easy way to sort out problems like this, unfortunately. Validating the CSS code is also a good idea - although it's the same as the other, that not all errors are a real problem. But the validator quickly finds everything -- some of which might be relevant, so it's a useful tool.
Also, if you are not using it, Firebug is a really great tool for working with CSS, so I'd recommend that as well.