I noticed my 2 month old had trace amounts of poop on his hands and may have put his hands in his mouth. Should I worry?

No, but. .. 2 month olds don't know any better, so it's important they wear diapers that you'll likely change often! Also, clean their hands and other 'dirty areas' with mild soap and water. Don't be angry with them, just continue to practice good hygiene. Have fun with him, it's a great time to take videos and photos during this first year; they grow so fast!