If I signed a contract for advertising but the publication keeps making mistakes and hasn’t followed through on promises made, is this grounds for cancellation of the contract?

You can sue the publication for breach of contract.  Your damages (monetary compensation you are seeking in your lawsuit) may be difficult to document because it would be lost revenue and you would have to establish that specific customers were lost if this is a new business.  If this is an established business, you may be able to recover lost revenue if customers were lost due to the mistakes in the ad.

If you decide to advertise with another publication and that publication charges more than the current publication which breached the contract, your damages would be the difference in the contract price between the former and new publication. You will need to mitigate (minimize) damages by selecting a comparable publication for advertising and a similar type of ad.  If you were to select the most expensive publication you could find and/or had much larger, more expensive ad, you failed to mitigate damages and your damages will be reduced accordingly.  

Rescission (cancellation of the contract) would be applicable as an alternate remedy.  Rescission includes restitution which means that if you received anything under the contract, you would need to return it or its value to the publication.