Semi-gloss paint dries with a slight shine, so imperfections that occur during painting become obvious when the paint dries. Using a roller with a long nap causes spattering, bubbles in the paint and potentially poor coverage. It can also create the appearance of texture, left behind from the texture of the roller. A short-nap roller produces a smoother finish with semi-gloss and gloss paints. Roller nap should be around 1/4-inch thick for semi-gloss paint projects.
The quality of the roller directly affects the paint finish, especially with gloss or semi-gloss paint. A poorly made, inexpensive roller often leaves behind fuzz, which becomes quite obvious on a semi-gloss finish. Low quality rollers also produce uneven results and don't last long. A good quality short-nap roller is the key to a good-looking semi-gloss paint finish. Compare rollers before purchasing one -- the inexpensive ones often have flimsy cardboard cores while the better ones use sealed cardboard or plastic. The material on a better roller looks nicer and more durable as well.
While it's a good rule of thumb to use a short nap with semi-gloss paints, the texture of the project surface is important as well. Paint applied by a short-nap roller won't cover an extremely rough surface as well as a longer nap. If you're painting a rough or porous surface, apply a primer coat to seal it before applying semi-gloss paint with a short-nap roller.
Even with a quality short-nap roller, improper roller use with semi-gloss paint can produce poor results. Painting too quickly results in a spattered finish and potentially poor coverage. Using too much paint may result in drips and non-uniform paint thickness. Using a roller with old semi-gloss paint may also result in an imperfect finish, as old paint doesn't blend as well as newer paint.