All too many folks find their way to these forums because they have problems and the first thing anyone hears is complaints.
So I'll start with a Thank You!
I've been playing around with a half dozen different store-front/shopping cart options and I found each one to be either too cumbersome or lacking what I consider to be the basics. Until I tried Abantecart. 

I've found the forums here to be a useful support tool but I couldn't find a solution to my current problem. I'm seeing the "Unknown AJAX Error" in a few places. Most notably when clicking a button in the "Main Page Banner Slider" and when adding an item to a cart when using a text entry option for that product. This was documented in a recent thread but I'm starting a new topic since we're at 1.1.9 now.

Checking FireBug I found two red warnings in the console when clicking the Add To Cart after entering something in a text input option:
  POST ... /index.php?rt=r/product/product/get_option_resources&attribute_value_id=8646
  POST ... index.php?rt=r/product/product/calculateTotal
Neither post seems to have a response.

There was no message in the Firebug Console when clicking a text button in the banner slider.

I couldn't figure out any cause for the error so rather than try to dissect the Java/AJAX I removed the display of the errors instead.

Edit:
  \storefront\view\default_html5\javascript\custom.js
Comment out line 71:
  // showMsg( 'AJAX Error', error_text, function () { } );

Whatever this error actually indicates, there does not seem to be any problems with the operation of the site. I'm willing to pretend the messages aren't there just because I can't see them. 

Hopefully this helps someone either debug the error or work around it.

-Eric