A few points need to be made here.
 
First, RIP to the victim in BHM.
 
Secondly, I would say it is 
NOT a mistake showing up to fly an airplane under the influence. Alcoholism is a disease and showing up to work with alcohol in the system is a by product of that disease. I'm not saying what happens is right and jail time is the punishment at times, but I would not categorize that as a mistake, it is a symptom of the disease.
 
Thirdly, in the United States it boils down to intent in our justice system when an accident happens. Basically the assumption our legal system takes is that everyone is trying their best to avoid an accident and that if a mistake does happen where people get hurt, well, it was a tragic accident. Cases in point, the pilots of 3701 did not intend to take off on the wrong runway killing everyone, the pilots of the American Airlines MD-80 in LIT did not intend to exit the runway, the pilots of the SWA flight in MDW did not intend to land long exiting on a street, the engineers that designed the DC-10 Hydraulic System that caused the Sioux City Accident did not intend it to fail, or the Boeing Engineers that designed the center fuel tanks for the 747 that contributed to the TWA 800 Accident did not intend it to fail.
 
The article 
Bandit_Driver cites has a lot of flags that raise my eyebrows. Flying 50 feet off the ground can be seen as negligent behavior and there was some confusion about what the pilot was doing there (was he taking money as a private pilot?), so there may be something more in that example.  If one wants a good example of what constitutes negligence in the United States take a look at two examples.  The 2005 Teterboro crash of a Challenger which 
SteveC, 
TFaudree_ERAU, 
mikecweb can probably add some details to...
 
http://www.nj.com/news/index.ssf/2010/11/jury_in_teterboro_plane_crash.html
 
http://www.nj.com/news/index.ssf/2009/11/pilot_in_teterboro_airport_cra.html
 
and the ValueJet crash in the Everglades...
 
http://en.wikipedia.org/wiki/ValuJet_Flight_592
 
http://www.nytimes.com/gwire/2011/0...rash-airline-mechanic-771.html?pagewanted=all
 
ATN_Pilot can probably go into more detail there but notice how the airline was NOT prosecuted, only SabreTech?
 
Fourthly, there are countries that 
DO throw pilots in jail for mistakes and they have horrific safety cultures. A lot of the Napoleonic Code countries do and places like China and Russia. I talked to an ALPA Air Safety guy that talked to a crew that had an altitude deviation in China. When they landed they were thrown in jail with the language barrier and the fact that the ATC tape could not be 'found' by the Chinese, it is very well possible that the crew heard one thing that the Chinese ATC was saying, but the ATC person did not know he was giving the wrong/different clearance. Also, look at the saga that the Legacy Pilots faced after the GOL Mid Air. Look at places like China, Russia, and Brazil, the United States is so much safer to fly around than those places and that points to the next point
 
Finally, throwing pilots/controllers/mechanics/engineers in jail for honest mistakes is horrific for the cultivation of the just safety cultures we should all strive for. Mistakes happen, sometimes tragic, but we should all learn from our mistakes and be able to share them without fear of reprisal. If one has an overrun on a snowy runway where no one gets hurt, the crew needs to be debriefed, see what happened, and changes made to the system to prevent it from happening again where some people may get hurt. If we throw people in jail for instances like this, where they had good intentions, we will be taking huge step back wards in aviation safety here in the United States.