I have an H&R Officer's Model. Believe I am the 3rd owner. Have not loaded Black Powder or lead bullets, just smokeless and jacketed and copper plated bullets.
With the issue iron sights, my better groups were with the Remington 305 g HP and IMR 3031 or SR4759 -- cannot recall exactly which and would need to go through my previous years' targets to find out exactly. I only shoot from the bench due to a medical malady and found the rifle shoots better with the cleaning rod removed for bench shooting. Since the Remington 300 HP is just about unobtainium, I tried a few loads with the 350 g Berry Copper Plated Bullets FP. Have not done any real load development for that bullet, just tried to get a 100 yard sight setting. Plus the light is not the best this time of the year in WA for shooting iron sights.
As for the rear sight, it does not have a threaded screw adjustment for elevation. You must loosen the eye cup and move it up/down. Problem: to adjust for wind, you also loosen the eye cup and move it right/left. Be very careful when making changes for range or wind. I leave it set for 100 yds., no wind. I could not see the copper/gold bead front sight and replaced it with a spirit level aperture from Lee Shaver. Have searched to no avail for a rear tang with a threaded screw elevation adjustment.
As for the action "popping open", it can happen. Think that is why the previous owner sold it to me. Since I do not hot rod the rifle I 'nevva' gave it a thought. However, when I had the gunsmith (John Taylor, Taylor Machine Puyallup, WA) install the new front sight, I asked him 'bout it. He said it can happen, it is an "easy fix" as the cam set screw needs to be kept tight. Believe said he tightened the OEM screw then added another to prevent the OEM screw from backing out as well doing as something else. While the H&R has the 1884 design with a stronger breech, H&R took a manufacturing short cut on the cam. Did some Googling and found a thread on this issue: I'm looking for info on Trapdoor repro. - The Firing Line Forums
I enjoy shooting the little carbine. Just wish my eye sight was better. If the price is right, the barrel and crown are not pitted, worn, wood is good, etc., consider making the deal. I think you will enjoy it. If I came across another officer's, or an infantry rifle, or the cavalry carbine, I would be sorely tempted if the price and condition were commensurate.