Culwathion, Good but tough question to answer - paired up with a shooter with a good set of eyes and the right ammo the 39 is a very capable rifle. When I was honchoing the 39 club rifle matches I'd get back some very impressive targets.
1" at 25 meters with open sights is very good, not many shooters manage that especially with the open sights. Good ammo would likely shrink that further. A peep sight would take some of the pilot error out of the equation and likely further shrink the groups or at least reduce fliers. Using the excellent Skinner peeps on my 39, 1895 and 336 Marlins improved my groups and greatly reduced eye fatigue during long range sessions. Like the open sights, it took me a while to adjust to them but once I did I've shot my best ever iron sight groups with them.
Accuracy is relative: I have a CZ 452 American with Leupold glass that with good ammo will put them in one hole at 50 yards off the bench. It is an excellent rifle but I hardly ever shoot it because the ammo it likes is expensive and with the cheap stuff my Marlin 39's do just as well. I also don't like carrying it in the field because not only is it heavier and bulkier, I don't shoot it any better offhand - which is 90% of the shots I take in the field.
50 yards, front rested CZ 452 American with 3-9X Leupold AO scope, RWS target ammo
Three shots, offhand at typical Grouse hunting range. The Grouse didn't want to play this day so my 39 and I did some plinking.
The 39's I own/have owned pack easy in the field and have an uncanny ability to put Grouse on the menu. They are also wonderful for plinking targets of opportunity and do very well in silhouette competitions (offhand at targets at 40,50, 75 & 100 meters).
Federal Bulk ammo, 50 yards, front rested, Marlin 39 open sites. I don't do this everytime but it ain't the rifle...