Big Brother is describing End Shake and he is correct in that it can cause misfires. Typically End Shake of 0.002 inch or more should be corrected. The method for doing this historically was by peening the yoke tube to "stretch" it and then re-cutting the end to fit. More recently End Shake shims made from hardened steel have come on the market in 0.002 inch increments making correcting End Shake a matter of removing the Ejector Rod and dropping in a shim in the bore for the enjector rod in the cylinder. These shims can make for a quick and cheap solution so it's a viable option if you are "handy".
Second potential cause is another cheap solution. Strain screws can have the tip peen with use. This has the effect of shortening the strain screw and the fix is to replace the strain screw with a brand new strain screw. BTW, on used revolvers with misfire issues it's pretty safe to assume that the strain screw has been filed at some point, so replacing that screw is the first step for curing a misfire problem. If your model 19 has a strain screw that has peened over or been filed you'll notice the effect very quickly the first time you pull the trigger with a new strain screw in place, because it will get noticeably heavier. For a 19-3 you can safely file that strain screw to produce a DA trigger pull in the 9-9.5 lbs. range and get reliable ignition, so if you find that trigger a bit too heavy you can tune it lighter. However, don't try going too far and an accurate method for measuring trigger pull is something I feel is near critical for tuning triggers. BTW, I use a Lyman Digital, it's easy to use and accurate for triggers of 12 lbs. or less. I'll also note that due to shipping charges I tend to order multiples of critical parts and stash them, last time I ordered strain screws I bought 6 of them.
Next down the list is a mainspring issue. IIRC the factory mainspring is only about 7 or 8 dollars, so they aren't very costly. If you are going to order new strain screws you might as well order a new mainspring at the same time. However, IMO it's actually pretty rare for a FACTORY mainspring to need replacement, by design they are not flexed enough to wear out very quickly. However, aftermarket mainprings at a lighter weight are common so it's not a bad idea to change out the mainspring at the same time you replace the stain screw, especially if you purchased the gun used. BTW, replacing the mainspring can be done without removing the sideplate but you have to fish it in blind. I remove the sideplate to make it easy and if you haven't ever removed a sideplate be sure to ask because there is a trick to doing it correctly. BTW, you tap them free, you do NOT pry them off.
Final area to investigate is the hammer Pivot Pin. Specifically you need to remove the hammer and examine the hammer, frame recess, and sideplate for a heavy rub. If you find a heavy rub look closely at the hole in the sideplate for the hammer pivot pin to see if it's egg shaped. In this event the news isn't good. It indicates that the hammer pivot pin is bent and the hole in the sideplate has "worn in" to this condition. The fix will require installing a hardened bushing in the sideplate and installation of a new hammer pivot pin in the frame. On the plus side this is a VERY rare condition for a revolver that wasn't dropped, so it's unlikely you'll have this problem. However, some level of hammer rub is fairly normal and a light rub can be fixed with the addition of a very thin shim in the correct position. It's unlikely a light rub will cause misfires but it can be unsightly so no harm in adding 0.002 inch of shim if that rub bothers you.
