Obviously theres a huge list of convictions that could prevent you from being employed and it would be up to the discreation of the airline.
I would imagine Drink Driving would probably prevent you, as it appears on any disclosures for up to 10years.
Speeding deppends on how the officer dealt with it, if you are done by fixed penality notice then its a traffic offence, if you are done by the court it becomes a criminal offence.