The semi-auto is one of the most wonderful actions in the world - when it works. Some designs function perfectly almost always (the AK-47 comes to mind). Others are more finicky and have been known to cause problems. As with any other thing, not all of them are created equal.
Accuracy with a semi-automatic rifle will vary from terrible to fantastic, depending on the rifle's condition, design, and type of ammunition used. The semi-auto may be the least consistent of all rifle actions, from one model to the other.
Semi-auto pistols are similar in that some are not accurate, others are. Some are dependable, others are not. John Browning proved about a century ago that a semi-automatic pistol could be made to be extremely reliable, and accurate enough for military use... but this is not always the case.