What security flaw exists in MAC authentication scenario?
Digital signatures are used to solve this type of problem. That is, a way for $A$ to sign the message for $B$ so that $B$ is highly confident that $A$ signed the message in question. There are lots of signature schemes out there, such as RSA signing, DSA, and others.

A MAC is not strictly a digital signature, but has a subset of that functionality and may meet your stated goals. It meets the requirement that an attacker won't be able to forge a new MAC without the key, which was the second point listed. (See this tangentially related question about HMAC.)

However, a MAC doesn't strictly meet the first stated goal. The problem is that MACs are based on symmetric keys, which means that everyone with the key can "MAC-sign" a message. When verifying a MAC, all the receiver ($B$) knows is that one of the parties with the symmetric key "signed" the message, but it don't know which one did. A copy of $B$ may send MAC-signed messages to other copies of $B$ and nothing distinguishes those MAC-signings from $A$'s MAC-signings. Practically speaking, this means, at a minimum, the attack surface of which compromised hosts can impersonate $A$ is widened. You no longer have to trick $A$ into signing malicious plaintext in order to forge $A$'s MAC-signature (such as by hacking it), using copy of $B$ will suffice.

This can have horrible implications if messages from $A$ are audited later and need to be verified as originating $A$ under the assumption of foul play on the network. (Maybe a legal court audit, perhaps just verifying that data collected was collected at $A$, etc.) Since any $B$ can forge a message on $A$'s behalf, you can't prove $A$ sent the messages. However, this may or may not be a concern for you.