If I had my windshield replaced but the glass company slit my dashboard over 12 inches, what are my legal rights as a customer?

You can sue the glass company for negligence.  Negligence is the failure to exercise due care (that degree of care that a reasonable glass company would have exercised under the same or similar circumstances to prevent foreseeable harm).

In order to prove negligence, you will need to prove duty (of due care mentioned above), breach of duty (failure to exercise due care), actual cause, proximate cause, and damages.

Actual cause means but for the glass company replacing your windshield, would your dashboard have been damaged?  If the answer is no, which appears to be the case, actual cause has been established.  Proximate cause means are there any unforeseeable, intervening acts which would relieve the glass company of liability?  If the answer is no, proximate cause has been established.  Damages means the amount of compensation you are seeking in your lawsuit for negligence.  Your damages would be the cost of repairs to your dashboard.  You will need to mitigate (minimize) damages by selecting a repair shop to repair your dashboard whose charges are comparable to other repairers of dashboards in the area.  If you were to select the most expensive repair shop you could find, your damages would be reduced accordingly.  If you need a rental car while your car is being repaired, you will need to select a rental car with a reasonable rate.  If you were to select the most expensive rental car you could find, you failed to mitigate damages and your damages would be reduced accordingly.

You may be able to file your lawsuit in Small Claims Court.  Your damages should also include court costs which would include the court filing fee and process server fee.