Whether you're submitting a theme to the Shopify Theme Store, or launching one for your own shop, you'll need to answer "yes" to the following questions:
Is all included material original?
Do all links work?
Is copy edited and error free?
Does JavaScript behave as expected, and with a minimum of resources?
Do pages load quickly?
Does the site work in Chrome for Mac - Current Version, and one previous versions?
Does the site work in Chrome for Windows - Current Version, and one previous versions?
Does the site work in Firefox for Mac - Current Version, and one previous versions?
Does the site work in Firefox for Windows - Current Version, and one previous versions?
Does the site work in Internet Explorer 7,8,and 9?
Does the site viewable in Internet Explorer 6? (It doesn't have to look good, just work)
To improve usability and reach a wider audience, we suggest you also check:
Does the site work on Android devices?
Does the site work on iPad?
Does the site work on iPhone?
Does the site work in Safari - Current Version, and two previous versions?
Do images have alt-text?
Is the site usable at 1024x768?
Is the site usable at 1920x1080?
As an experienced Shopify template designer, you're already doing these things. :)