Missing education information in the previous visa application

I currently have a visitor (B1/B2) visa. In the DS-160 form for it I haven’t listed all my previous jobs (I had 4 for the last 5 years, but I listed only one) and forgot to mention my bachelor’s degree. I thought it isn’t important for a visitor visa.

I’ll be applying for H1-B and I have to mention my previous visas. Does it mean that my previous DS-160 will be inspected? If so, could missing bachelor’s degree rise a problem?