If you got an inadvertent dural puncture with epidural anesthesia, what happens?

Depends..... It ranges from nothing to headache, infection causing meningitis, encephalitis............... Most of the time nothing or headache treatable with tylenol (acetaminophen).... Remember it is now lumbar puncture instead of epidural injection as far as medication is not injected !
See below. If there is an inadvertent dural puncture there may be a low leak of cerebro spinal fluid from the spinal canal. This can cause a headache that is worse when the patient is upright. This problem usually resolves after one week. It can be treated conservatively with fluids, caffeine and rest. It can also be treated by an epidural blood patch.
Needle tear dura. Placement of an epidural during labor is done completely by feel. The so called epidural space is very small and if the needle goes through the epidural space without stopping, a dural puncture occurs.
You will probably. get a bad spinal headache, the epidural needle is very wide makes a large hole and CSF leaks. When the membrane is punctured intentionally a narrower needle is used greatly decreasing the chance of leakage and a headache or is much milder.
Maybe a headache. When this happens, the needle actually enters the space where the spinal fluid circulates instead of staying within the epidural space. This can cause a headache, which isn't dangerous but can be a fairly severe headache. Usually it will go away on its own. Sometimes other treatment is needed if the headache is severe; the most common is called an "epidural blood patch".
Sometimes nothing... sometimes a headache, which can be treated. Dural punctures are performed all the time on purpose for diagnostic purposes, so an accidental one is not a major problem.