The extrasolar planetary system around HR 8799 is the first multiplanet system ever imaged. It is also, by a wide margin, the highest mass system with >27 Jupiters of planetary mass past 25 AU. This is a remarkable system with no analog in any other known planetary system. In the first part of this paper, we investigated the nature of two faint objects imaged near the system. These objects are considerably fainter (H = 20.4 and 21.6 mag) and more distant (projected separations of 612 and 534 AU) than the three known planetary companions b, c, and d (68-24 AU). It is possible that these two objects could be lower mass planets (of mass ~5M _Jup and ~3M _Jup) that have been scattered to wider orbits. We make the first direct comparison of newly reduced archival Gemini adaptive optics images to archival Hubble Space Telescope/NICMOS images. With nearly a decade between these epochs, we can accurately assess the proper motion nature of each candidate companion. We find that both objects are unbound to HR 8799 and are background. We estimate that HR 8799 has no companions of H < 22 from ~5'' to 15''. Any scattered giant planets in the HR 8799 system are >600 AU or less than 3 M _Jup in mass. In the second part of this paper, we search for any sign of a "reverse parallax signature" in the astrometric residuals of HR 8799b. No such signal was found and we conclude, as expected, that HR 8799b has the same parallax as HR 8799A. In the third part of this paper, we carry out a search for wider common proper motion objects. We found one object within 1 deg² in the Palomar Observatory Sky Survey-Digitized Sky Survey images with similar (<2σ) proper motions to HR 8799 at a separation of 40. We conclude that it is not likely a bound companion to HR 8799 based on available photometry.