The new rifle Gene Hackman tells his associates they will use "is a Sharps-Borchardt Model Creedmoor rifle." When he shows the rifle up close and cocks the action, one can recognize it is a Providence Tool Company Martini-Henry Mid-Range, a totally different gun.
Gene Hackman's rifle (the caliber of which was unclear) is sufficiently powerful to kill from several hundred yards, yet he presses his eye against the scope eyepiece with no consequences. Any rifle that powerful has a significant kick, one that would have certainly damaged both his eye and the surrounding area.
When Frank shoots Doc (5 times rapid fire) he uses a Colt Peacemaker model which is a single action pistol. The only way to rapid fire a single action pistol is to fan the hammer, which is very inaccurate, and since his left hand is holding down his right wrist, it is not possible for him to fan the gun.