I would agree with Dr. Rand. Having seen several questions that you have recently posted, while all very important and meaningful questions, if you are having this much indecision and concern, I would suggest just not doing anything.
As to your current question, facelifts are very safely done in an ambulatory surgery center (ASC) setting all of the time. In my practice, all of my facelifts are done in an ASC without overnight hospitalization.
As to your questions about a hospital:
1) There is a considerable body of evidence to show an increased rate of complications in hospital versus ASC facilities. This is a general statement and may not apply to the particular facility where you are having your procedure. You can always ask the hospital for their infectious complication rate.
2) Medication errors are a risk in hospitals and ASC settings. I would not use this is a concern.
3) Malfunctioning equipment is also a concern in any setting. Though I know of no direct evidence, my feeling would be that hospital would be less likely than an ASC to have malfunctioning equipment. Hospitals are generally accredited by JCAHO. This body is well known as the most stringent of any accrediting board for hospitals and ASC facilities. In addition, most hospitals have on site biomedical technicians to perform repairs. Therefore, if there is a malfunction during surgery, hospitals are in a much better position to deal with the problem than an ASC who generally contracts with an off-site vendor to perform repair and maintenance.
4) Training programs are not at every hospital. In fact, I work at three different hospitals in a suburb of Dallas and none of them have fellows/interns/residents (except for the fellow which works with me). Even at teaching institutions, the interaction of trainees with cosmetic surgery patients is generally limited.
5) Cost: You are correct that hospitals will be more expensive than a surgery center. I have found, though, that this increase in cost is rather minimal in the hospitals I deal with. With the costs I have seen, I believe it more important to choose the physician and not be overly concerned about the added cost of the hospital.
6) Overnight stays: While I do not believe that an overnight stay is warranted after any facial cosmetic surgery procedure, it is not inapprorpriate by any means. In some cases, patients request an overnight stay to have someone help them with aftercare. In my practice, if a patient requests assistance, I arrange either a hospital stay or a private nurse at the patient's home or a local hotel with a suite or adjoining rooms.