The same law firm is representing both me and my company in the H1B process. Will this be a problem?

It is very typical that one attorney represents both the employer and employee in an H-1B filing. It is not a conflict if both parties consent to the representation. There could be a problem in the future, if for instance, you seek other employment or want to "port" to another company and you seek advice from the attorney. The attorney must disclose any information like that to the company as well since he represents both parties.

Actually, it is very routine. As counsel above suggests, should circumstances change so that the interests represented potentially conflict, the attorney is ethically and legally obligated to make full disclosure.