My dentist did an IPR on my tooth today and one looks cracked. Is it cracked and is it the dentist's fault? (Photo)

The only thing to evaluate is that if the doctor has those pictures before doing the proceedure , there you can see if this crack was before the ipr , and then you can discuss if there is any responsability, ussually this lines exist previously but you do not notice them , until you take a good look to them .

Good news!  Your tooth does not appear to be cracked from what I see in the photo.  What I do see is a natural craze line.  Craze lines are insignificant and do not cause problems with the tooth.  IPR (inter proximal reduction) is often required in orthodontics to achieve the desired results.  The benefits far outweigh any risks.  IPR relieves tight contacts and creates space so that teeth can move into the ideal position.  Straight teeth are healthier, less likely to crack and less likely to develop gum disease.