It definitely sounds like a badly adjusted AF module.   If you have sent the whole set of camera+lenses for calibration, you can be optimistic about getting it back reasonably well adjusted.

24mp on aps-c is very punishing for even slightly mid-adjusted lenses so even when your camera comes back you may still find some lenses don't quite AF with 100% accuracy.  That's why you need AF micro adjustment such as in the a77.   Older Sony cameras had ways of DIY unofficial adjustment for the AF module, by turning 3 screws hidden near the tripod mount.  I successfully calibrated my a700 that way.  However, I don't know of any way of accessing the same sort of screws for the a77 or a65 as the AF module is now under the flash and inaccessible. 

I have the same issue.  I have just posted a reply on another thread in this forum (probably the wrong thread). Originally I thought it was user error, or a problem with my lenses, but I am sure I am using the correct settings and I get sharp results using the same lenses on my A200.  My additional problem is that I purchased my unit from a Hong Kong supplier and I don't want to return it to China (I have already had other issues with goods I have returned to China), so I don't know how to go about getting it fixed.  From what I can make out, there seem to have been a lot of A65s sent out with faulty AF.  What makes matters worse is that I have seen posts where users have returned their cameras for service, only for them to come back with no adjustment as they are deemed to be within industry tolerances.  A camera with this size sensor should have micro focus adjust capability.  A camera costing this price should have a correctly functioning AF system out of the box.  This issue is well documented, Sony seem to be doing nothing to address this problem.

Simon,

Thanks for your helpful reply.  I have been in touch with the supplier.  It seems I have a 2 year warranty with the supplier himself.  It looks like I am going to have to bite the bullet and send the unit back to him.  The warranty states it covers:

1. Manufacturer Defects (Known issues caused by particular product and various other ailments that can cause product to malfunction)  
2. Replacement of item if necessary
   • Items arriving damaged on arrival (it is our responsibility to ensure items are packed well before shipment)

...Once received, item will be inspected by our technical staff, and we will email you within 14 working days to describe errors found with the product and plans to fix or replace your item....   I advised him it was a back focus issue and asked if he could resolve it, he replied:  'After we receive the camera from you. We will send it Sony service to repair as soon as possible.' !   I just hope when it comes back, that it is not deemed to fall within industry tolerances.  Thank you for your interest.