You audit Monero the same way you audit Bitcoin. You run a node.
The code is completely FOSS.
No Bitcoiner is taking advantage of Bitcoins transparent/simple math to scrutinize the blockchain anyway so that doesn't help you. Are you making sure every block that all input = all outputs? No, you just run your node and pay no mind. So in practice what is the difference?
Monero audits supply using bulletproofs and pedersen commitments. It is well established and sound cryptography from the 80s, but admittedly more complex than bitcoins simple math.
An exploited inflation bug would be equally catastrophic once it happened to either Bitcoin or Monero. Attackers have the advantage. There is no good solution to fix an exploited inflation bug without hurting other users on either Bitcoin or Monero.
Trivia: Did you know there was a hidden inflation bug in Bitcoin only an anonymous user knew? They couldve easily exploited it, but very luckily they were an honest actor who secretly let the devs know (who couldve also decided to exploit it). If they did exploit it, how would detectable inflation help after the fact? It wouldnt.
https://bitcoincore.org/en/2018/09/20/notice/
Again none of this matters if you don't use Monero to save. So it's all moot.