See this -
www.fpnotebook.com/OB/LD/FrcpsAstdDlvry.htm
Kiellands forceps or high forceps are no longer used in most parts of the world. Simpsons and Andersons forceps are rarely used, because CS is preferred.
Outlet or Wriggleys forceps can still be used because by that time it may be too late for a section.
My obstetrician has always maintained that the riskiest way for a baby to be born is by means of a forceps delivery. Outlet forceps are not always bad (by that time it is too late for a CS anyway), but she has always told me that as a doctor she herself would never agree to mid or high forceps. These include the dreaded Kiellands forceps of course, but also the Neville Barnes, Anderson's and Simpson's forceps.
www.thieme-connect.com/ejournals/abstract/ajp/doi/10.1055/s-2003-42775
(states that forceps are known to cause brachial plexus nerve damage)
journals.lww.com/greenjournal/Abstract/1984/06000/Birth_Trauma__Incidence_and_Predisposing_Factors.7.aspx
(Logistic regression analysis of fetal, maternal, and intrapartum complications in labor and delivery revealed that midforceps, shoulder dystocia, low forceps, infants greater than 3500 g, and second stage labor exceeding 60 minutes were the predominant events associated with fetal injury)
journals.lww.com/plasreconsurg/abstract/1990/01000/facial_nerve_palsy_in_the_newborn__incidence_and.1.aspx
(states that facial nerve palsy is most common in macrosomic infants or those born with the aid of forceps)
facm.unjbg.edu.pe/revistaspediatria/Clinical%20Pediatrics/2004/Pediatric%20Clinic_51_June2004_%20the%20Newborn%20Nursery%20Part%20II/Management%20of%20birth%20injuries.pdf
^ Fabulous article about birth injuries. From what I could make out majority of the birth injuries had forceps listed as the major risk factor, other than of course fetal birth weight of more than 3500g.
www.sciencedirect.com/science/article/pii/0029784496001512
(lists forceps as a major risk factor for pelvic organ prolapse)
www.sciencedirect.com/science/article/pii/S0002937803005726
(there is an increased risk of anal sphincter damage and hence incontinence with a forceps delivery)
www.bmj.com/content/308/6933/887.abstract
(lists forceps as one of the major risk factors for third degree tears)