Have to agree with John Burke on this one. Sounds like you're making excuses, and that your former employer may be correct about some issues. Count yourself lucky you landed the new gig anyway, and use this opportunity to make yourself the "perfect" employee.
As for employers being careful as to what they say about former employees, I'm guessing that, sadly, is also true. I know a guy who has lost two jobs due to an over abundance of alcohol indulgence, but, yet, is able to move from job to job without the new employer finding out. Very upsetting that it is allowed to happen, but I'm guessing that the companies don't want to answer to the FAA, so they keep their traps shut.
Kinda got off subject there. Sorry.