A cracked manifold is easy to spot. Cold engine, spray bottle of water or a damp hand. Take off heat shield to expose manifold. Start engine and run to the passenger side. Make hand wet and feel for air leaking. Once the manifold gets too hot, spray a little water on it and watch the steam.
Do NOT pour water on the cast iron.

It is also possible that the flex portion of the exhaust is broken. If it is, you will notice exhaust escaping from there.

Not to doubt a $ealer, but they should have pointed out where the manifold was cracked.


EDIT:
The rear O2 sensor us covered by a plate under the car. Just behind the cat.

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Keeping it running is better than buying new