Point lights are "hot pixels." Many image editing programs include a tool to remove them at the click of a button. There are some related questions questions and answers [here][1].

Long exposures are also subject to dark noise. There are some related questions and answers [here][2].


  [1]: https://photo.stackexchange.com/search?q=hot%20pixels
  [2]: https://photo.stackexchange.com/search?q=dark%20noise