Applying early doesn’t mean just submitting your application. It means having your application 100% complete by the end of July. If any part of your application is missing, a school will put your application on hold and your application will not be evaluated until all the missing parts have arrived.
If the school is waiting for new DAT scores, they will get them shortly following the exam (approximately 3 weeks). Don’t worry! There will be plenty of spots left at every dental school. Many people submit their application in June prior to taking the DAT. It is a fairly common practice and as a result many people will be at the same stage.
If the school is waiting on letters of recommendation remind the writer that your application is already submitted and is currently on hold until all the components like the letter of recommendation are submitted. Do not pressure them! It was your responsibility to give them enough time to finish the letter. Pressuring them will only result in a poorer letter or remarks finding their way into your letter.