At almost every home inspection with a sump system, I end up recommending some type of change for safety, performance, or both. Here are five common sump system defects, in no particular order.
1. A loose or missing sump basket cover

This is a safety issue because a small child could drown if they fell in to a sump basket. The fix for this condition is quite simple; if there's no cover, install one. If the cover is loose, get a few 3" drywall screws and run the screws right through the cover in to the sides of the sump basket. A good rule of thumb is to also make sure the sump cover can support someone's weight, for obvious reasons.
Ideally, the sump cover should also be airtight. This will help to prevent radon gases from entering the home, as well as moist air.
2. A missing check valve
A check valve should be installed on the discharge pipe to prevent water in the discharge tubing from dumping back in to the sump basket after the pump shuts off.

This is also a simple fix; check valves cost about $10 and are easy to install.
3. An undersized discharge pipe

Sump pumps typically have a 1-1/4" or 1-1/2" outlet. The size of the discharge tubing should match this; that means don't use a garden hose. Using undersized discharge tubing, even at the exterior, will force the pump to run longer each time it turns on, decreasing the life of the pump. Some smaller pumps may come with an adapter for a garden hose, but those are the exception.
The fix for this condition is simple; use larger tubing. Inside the house, use ABS or PVC tubing. Outside the house it's not nearly as important. Home improvement stores sell 25' lengths of corrugated tubing for under $10, and connecting these is a piece of cake.

4. Discharging water right against the house
When a sump pump discharges water right up against the house at the exterior, where does the water go? Right back down in to the sump system! While this might seem to be extremely obvious, experience has told me that it might not be, because this is a very common defect. The discharge tube from the sump system should terminate at a point where the water will drain away from the building.