It is correct that the Error Console is opened via Tools > Error Console. You can select for only errors, and copy/paste the messages here.
With regard to Google-analytics.com, if you don't want it to run, just leave it in the default blocked zone, or mark it as Untrusted. NoScript will run a
Surrogate Script that will make the page happy, while sending none of your personal information to Google. This doesn't require ABE at all.
The surrogate should prevent the need for any exceptions. Is there a reason that you want the real G-A to run at certain sites?
I don't see any connection to HOSTS file in your posts, unless that was the URL REMOVED part.
With regard to your original question, NS is not the likely culprit, but there's an easy way to tell:
If one of the affected sites is a trusted site - *all* scripts there are in your whitelist, -- then go to NS Menu > Options > General, and click "Scripts globally allowed (dangerous)". Also, on Options > Embedding, uncheck "Apply to whitelisted sites". Perhaps your trusted online bank might be a good test site. Go there, and if the problem persists, NoScript has been exonerated. If that solves the problem, then there may be a NS issue to explore further.
Remember to uncheck "Scripts globally allowed", and re-check "Apply to whitelisted..." (if that is your preference -- it's mine) before going anywhere else.
Let us know the results.