What will effect me getting a UK work permit?

I am a US citizen with a graduate degree who got picked up to work in the UK with UBS for one year (internship). They have applied for my work permit but I want to know, what kind of things could disqualify from getting the permit? In reading their liability waiver in regards to the permit, it says convictions would effect my chances. I looked up my record and have 2 speeding tickets that I paid off from over 3 years ago (both of which where exactly 9mph over) and was caught smoking when I was younger. The smoking part didn't lead to a conviction as I did some community service and is in the process of being expunged. Should I worry abut getting in or try and call the emby and see what I can do.