DOES THE DOCTOR SIGN OFF PROGRESS NOTES OF AN ADMITTED PATIENT AT THE HOSPITAL ON THE SAME DAY THAT IT IS WRITTEN?

Although the practice may vary from state to state, or even from hospital to hospital, it is not unusual for a physician to sign a note, especially a computerized note, after the fact.  You would need to see the facility's policies and procedures (of the Department of Medicine) to learn if this practice is appropriate or not. The P and P's may not even specify.  In such an instance the only way you would learn if the note was accurate (or, for example, altered to suit the physician's version of events after the fact) would be to take their deposition under oath about the circumstances surrounding the note.  Good luck.