Chubbo, First thing I would like to recomend for anyone who owns and shoots a 1858 Remington is to try to find and buy a book called "Black Powder Hobby Gunsmithing" By Sam Fadala and Dale Story. The book is one of the best I've ever seen for any black powder shooter and it devotes a whole chapter on how to tune your own 1858 with great pictures and step by step instuctions.
It's out of print the last time I checked but it can be found on the internet "Out Of Print" book stores with a little searching.
One thing to remember is that the reason these guns are so cheap is because they don't take the time to polish them or check tolerences like they should. That being said if you take the time to do it yourself and do it right you will have a top class weapon that's worth 4 times what you paid for it.
You can go as far as you want to fancy it up or just take some time to have it working really smoooth.
First thing you need to do is totally strip the gun and find something to keep all the little screws and parts in.
Now take the nipples out of the cylinders. Rub your fingers across the star of the cylinder (The end that faces the hammer) and you will feel that it's a bit rough. Place it in a vice but wrap it with a rag or a couple pieces of soft pine wood first to protect the finish from the jaws.Take a bastard file and keeping it as flat as you can stroke it across the stars until they feel really flat and smooth. Go slow and keep checking it as you do. Then polish it with 600 grit water paper. Oil it good and set it aside.
Now take a look at the cylinder rod and you will see that the finish on it is a little rough also. Useing the 600 grit paper keep sanding the hole lenght of it until it feels smooth to the touch, oil it and set it aside.
Adjusting the hand is something you want to go slow and easy with and only get rid of the rough edges. I like to use a stone for that or a file.Make sure all burs are gone and it's smooth all the way around but don't over do it. Oil that and set it aside.
Next you want to polish the cylinder bolt. This is what locks your cylinder in place and it must be smooth as a babys butt all over. Use your file and paper but don't get carried away, Just polish for now. Oil and set it aside.
Next is the hammer. Feel the hammer on the sides as well as the caugs and get rid of any burs with a file and polish with paper. Do not take to much off the caugs , just polish for now. Oil and set it aside.
Now the trigger. Do the same to it, just smooth and polish and make sure there's no burrs or high or rough spots.
Now put just a little grease on each part and put it all back togeather and see how it works by repeatedly cocking and letting the hammer down easy. If the cylinder still seems tight then take out the cylinder and see if it need a little more polishing and also the cylinder pin.
Before and while you are shooting it for the first 2 cylinders I would use bore butter on the barrel before every other shot.Just make sure you remove the cylinder before you run a patch down the barrel to avioid any accidents. This helps "cure" the rifeling and the steel in the barrel. Make your first loads about 20 g. 3f Goex with a woder wad over the powder then the ball and then grease over the ball. Wonder lube works great. Once you get it broke in you can use any of the other methods and concochtions you read about on here,Lol. Thay are all good and you may come up with your own ideas as you go along.
If your not sure what parts I'm talking about here just look in your manual and they have a break down in the back with the name of parts.
There are many other things that need to be done to the 1858 to get it really smooth and operating as it should but it would take a book to explaine it all and that has already been done by others.If you decide to really work it over then get a few books on the subject and ask as many 1858 cowboy action shooters as you can what they do to there's.
I haven't had a cap fall off before I shoot or one jam my gun in years due to polishing the rough edges and rounding of the open area (Ports) around the nipples and also chamfering the end of the nipples. The trick is when you put the cap on you need to "seat it" by useing a 3/8" 6" long doll rod with a small round piece of leather on the end. After you place the cap on the nipple shove it home firmly with the rod.If you have to pinch the cap to make it stay on then you have not seated it all the way or you have the wrong size cap.
Chamfering the end of muzzle of the barrel and the breech will give you better accuracy due to easier loading from the cylinder to the ramp as the gun is fired. Chamfering the muzzle will make sure there are no burs on the end to throw off the ball as it leaves the barrel. All this needs to be done with the right tools and it is all in this book as well as others.
If you mess up any of the pieces as I have through trial and err you can buy a parts kit from Cabelas but it's not listed in there book, you have to call them and ask for it.It's really cheap and you should have one anyway because loseing parts or breaking one when you want to shoot is a pain in the butt when you have to wait for parts.
Hope all this helps a little , Mike
The thing that surprises me is that it doesn't seem to affect the accuracy at all on these Remingtons. Did allot of work on mine as far as spit and polish goes and a few other little tricks to make it run so smooooth, but it sure is fun to shoot and becomes even smoother all the time. 
Really don't notice much difference in accuracy but it lets you know that it's a cannon!, Lol.
My son has that one.