The trigger guard screws.....This area is the one weak point of design on all half stocked rifles, not just BSA's, I have given up counting how many times I have been handed / shown vintage BSA's that have loose screws in this area from lack of maintenance. When I was a nipper, every gun would come with a booklet explaining the need to check all screws frequently, or better every time the gun is used.
(I am talking above about guns in otherwise good condition, just badly maintained...ie, the screw threads are fine, but the owners don't realise what a hammering spring guns give their fasteners).
There are guns out there (and shown in books) where there is a third screw (larger countersunk) through the top of the cylinder into the threaded portion of the trigger block, I don't know if BSA experimented with doing this, or whether it was a fix for "loose" guns though.
Anyway, I cannot emphasise this enough, shooting a gun, even a few times with screws loose will cause problems, which quickly can become serious!
The cylinder to trigger block fit is also affected by bad maintenance, so it is common to see guns with this part loose as well (on little used guns this fit is very good).
I have seen PTFE tape used on the cylinder threads to help stabilise this joint, and myself have used locktite on one particularly bad example I re-built (not to be done lightly, as needs careful application of heat to undo, but the gun was otherwise good, and was all new inside, so worth saving.
Remedy......once stripped, a fairly good repair for the home gunsmith is to open up the threads to 2ba size, use a 3.9 or 4mm drill, and preferable a quality 3 tap set to get full thread form.
The problem then is that screws have set sizes for proportions regarding the head against the thread so although 2ba slotted cheese head screws are easy to find, you may need to reduce the diameter of the head (at home I use a drill in a vise, and a fine flat file to rough shape, then emery on a block to finish profile screws...also works well on damaged screws as you get the same effect as new ones if carefully done).
The Vintage Diana Forum
The Vintage BSA Forum