What were the biggest problems in early 19th century surgery?

The biggest problems in early surgery were:

• Pain caused to the patient (the shock alone could kill some people)
• Bleeding (patients could bleed to death very quickly)
• Infection (blood poisoning and gangrene were common outcomes of surgery)

These problems were gradually solved in the 19th and 20th centuries.

• Two American dental surgeons Horace Wells (1815-1848) and William Morton pioneered the use of nitrous oxide (laughing gas) and ether respectively as anesthetics (chemicals that stop someone feeling pain during an operation).  There are now many kinds of gases, vapors and drugs used to ensure a patient is comfortable during surgery.
• Joseph Lister in the UK developed ways to cut infection by sterilizing surgical instruments, hand washing and using a carbolic acid spray (see machine above) to kill germs in the air.  Nowadays, air in operating theaters is carefully filtered to remove bacteria and a germ free area around the site of the operation (a sterile field) is maintained at all times.  Modern antiseptics include betadine - the orange solution painted around operation sites prior to surger.  
• Antibiotics such as Penicillin, developed in the 1930’s, mean few people nowadays die from blood poisoning and other infections.
• Research into the nature of blood including the imporance of blood groups, led to successful blood transfusions in the early twentieth century.  These have reduced deaths from blood loss hugely.