You need to check the Rehabilitation of Offenders Act for the specific crimes you have been convicted of. As far as I am aware, Driving While Under the Influence is a civil offence and is unlkely to prevent your employment, but Assault is a criminal offence which may very well do. Your main problem is not going to be getting past the selection stage for an employer, it's going to be getting through the hoops you now need to jump through to get an airside pass. Disclosure Scotland do the Criminal Records Check for all employees requiring a pass to a BAA airfield; they should be able to tell you when a conviction is spent for that particular purpose.
Scroggs