One problem that can arise from a bad carpet cleaning is rapid resoiling. This is probably the most common thing that can happen when a bad cleaning company cleans your carpet. They will typically use too much cleaning solution in an effort to speed up their cleaning. They might even use a chemical that is cheaper and not approved for carpet cleaning to improve their bottom line. The residue they leave will cause your carpets to get dirty very quickly. A good carpet cleaner on the other hand will thoroughly rinse your carpet leaving it residue free and clean for much longer.
The second problem that can occur with improper cleaning is mildew growth. This can occur if they soak the carpet so much that it does not dry for days. Many bad cleaners will use too much pressure on machines with too little vacuum so that they can get through your home faster. The result is a carpet that is thoroughly soaked. When it dries days later you will find it just as dirty as it was before but now with a musty odor. Professional cleaners can get your carpet dry in as little as one hour but will have it dry within about six hours. Anything more is unacceptable these days.
I am sure you can see that these are two very bad potential problems. This is why you need to take the time to find a good carpet cleaner. The time you spend researching will be well spent. Good luck.