For an egregious act:
* Outrage
* Abomination
* atrocity
* offense
* transgression
* misconduct
* infraction
* breach
For an egregious mistake:
* Blunder
* Fiasco
* Error
* Miscalculation
For an egregious display of something negative:
* Excess
* Extremity
* Outlandishness
* Absurdity
Ultimately, the best noun to use will depend on the specific context of what is being described as "egregious."