The parents of three-month-old Alexander Kendall, from Norwich, spotted the errors after being given a set of five bodysuits from the store.
One bore the slogan "I was born awsome", while the other read: "Daddys little man" - missing an apostrophe.
Tesco apologised after Alexander's father shared the errors on Twitter.
It offered a refund or exchange and said: "Sorry about this, we've made our suppliers aware of this so it can be corrected for future stock."
Mother Sophie Kendall, 28, said: "We both work as journalists so are perhaps a bit more pedantic about these things than most.
"Fortunately Alex is a long way off being able to read so we'll just use the suits and hope nobody notices."
Supermarket chain Tesco has said it will brush up on its spelling and grammar after making two mistakes in a single pack of baby clothes.