The answer to your question depends in part on the laws of the country in which the inn is located. Under most theories of common law, and particularly laws of the United States that govern landlord-tenant relations, an inn owner (in this case, the landlord) is responsible for injuries suffered by a guest (the tenant) if it can be proved that the injuries were caused by the landlord's failure to maintain the inn in a completely safe condition.
One of the complications of proving liability, and an important defence for the landlord or inn owner when such injuries occur, is the doctrine of contributory negligence. This doctrine requires that the person injured prove that he or she took no action that might have contributed to the accident. For example, if a guest ignores signs around a pool area that clearly warn about wet pavement and forbid running in the area--and is injured after running and slipping--the landlord can allege that the negligent actions of the guest contributed to the injuries.
If, however, the guest or tenant can prove that the accident and injuries were the direct or indirect result of improper maintenance or lack of warning signs or other types of negligent behavior, then the landlord or inn owner is generally held fully liable for the results.
The issue then becomes enforceability. In general, most such incidents are handled first by the landlord or inn owner's insurance company, and the goal of the insurance company is to settle the injured party's claim with the smallest payment possible. If a settlement cannot be reached, though, the injured party must file a lawsuit, and a suit can be expensive and time consuming. In most cases, slip-and-fall incidents are settled at the insurance company level.