how to avoid grid edit save based on the a field value

In grid edit mode, very limited validation is possible. If a field is mandatory (at the table level) and it is empty when saving, you can't save. Other than that, it will allow all other changes. To overcome this situation, I have come up with a work around. Not perfect, but something is better than nothing. I have a formula-text field "Error Message" which I use to populate with a message if something is wrong. This field will be on the grid edit report and every other report. The hope is that someone or the other will notice this and fix the data to get rid of the error message. When you are in form-edit mode, I can use the same field and abort the save if the error message field has contents. Having said this, I am interested to see if anyone else has other ideas.

Is it possible to set the custom role permissions for Edits on that table to only be permitted when the error field is blank?

It would prevent the user from editing that row of data in grid edit or on the form. 

You can certainly do that. Go to the table settings -> Access. Then for each role that you want to restrict, choose custom rule for edit permissions and state your condition in which they CAN edit the record. But honestly, I don't see how this would solve your issue. But you are in the driver's seat and it is your call.

Slider...An update to this issue: QuickBase is working on Data Validation (still in beta but available to you upon request). Using Data Validations, now you can actually prevent the data from getting saved if there are errors. You get to define what is an error and what is not and what error message to be displayed when there is an error. I am using this now and it works great.