Should I be worried about my background check?

I currently got a job offer from a high end company, who is known for being very thorough. I received a background check to complete through Hireright. I gave my employer a resume, and completed the background check to the best of my knowledge. What I'm afraid of is, that I don't know some of the actual dates. I could even be a year off, I honestly don't know. I don't have my tax forms or previous W2s to look at either. Secondly I didn't list all of my previous employers, I always left on superb terms, but I was going to school and would often have two part time temp jobs at once. I never thought them relevant. Mainly there are two important relevant jobs in my history that I listed and am unsure about the exact years (I answered what I thought they were and am afraid I could be wrong) I would contact these employers for my exact dates but both I had to leave because they were liquidated. Should I be worried?!