JV, the two things that come to mind immediately, are firing pin protrusion, and headspace.
Some rimfire rifles have a flat breech face, at the rear of the barrel, and a recessed bolt face, on others, the rim cut is in the barrel, and the bolt face is flat. A few, have recesses on both parts, but in every case, you need to be in the range of .041-.043", between the part of the bolt that touches the rear of the cartridge, and the part of the barrel the front of the case rim is pushed up against; more than this, and both reliability and accuracy will suffer. This is called headspace, and is checked with , obviously, headspace gauges, typically, a .041 'Go', gage, and a .044 'No Go' gage.
With the bolt 'uncocked', and, if of the 'inertial' type, the firing pin held forward, all the way, you want to see .035-.038" of pin, above the breech face of the bolt. Less, and ignition is unreliable; more, and you will damage the barrel, in firing, or even worse, 'dry firing', the rifle.
While the shape of the firing pin tip is a third possible cause for reliability issues, it is a never ending debate, among rimfire shooters, and gunsmiths, as to what is the 'best' shape, for any given rifle; it should NEVER be sharp, but, otherwise, if the above headspace and protrusion numbers are met, in an otherwise unaltered (Springs?) rifle, it will reliably fire!
Forster, Clymer, Brownells, to name a few, can provide you headspace gauges at reasonable prices, if you are doing your own work.
Hope this helps, Terry