Need Advice: To Upgrade? & All In One SEO overwritten??

Hello!!
I am updating the text, titles and meta descriptions on https://priosoft.com AND attempting to fix coding issues as I come across them. I have updated a number of the pages already – including the Home Page and have just noticed that the meta description is not pulling the new one that I crafted and populated into All in One SEO. Update . . . I THINK I HAVE THIS ISSUE RESOLVED BUT STILL WOULD LIKE HELP WITH THE UPDATE QUESTION.

I know that numerous files for this site were FTP’d directly to the server and am wondering if any meta data installed directly in an html file & uploaded could be overriding my changes in All in One SEO.

The website owner was uncomfortable updating the WordPress core files to 3.7.1 from 3.0.1 along with all of the plugins because this site is using a child theme built a long time ago.

Could this be the reason that my SEO tool is showing the coding errors increasing, rather than decreasing as I work them through?

What would be the best way to approach improving the SEO for this website? Is the update to WordPress imperative? What is the reason the old meta descriptions are showing up in the searches?

If anyone can shed some light on my situation, I would greatly appreciate it.
Thank you!!