Only have a couple hundred rounds through my SVT (1940 Tula with the old style brake, and matching stock # to the receiver), but I'm getting 4-5 inch groups at 100 yards out of it with the battle sights and surplus ammo quite consistently. That's about all I can get from ANYTHING with open sights, so that's telling me the rifle itself is more accurate that my 43 year old eyes can pull off.
The accuracy problems, from what I can tell, seem mostly related to poorly bedded receivers, and that's a fixable problem. If you're not worried about retaining the historical value, glass bedding the receiver is not particularly hard, and does wonders with most rifles for getting rid of the vertical stringing and shrinking group sizes down considerably. I'm very tempted, but have already signed on for a vintage rifle shoot with it later this summer, so can't muck the history on it. I expect to get my butt handed to me by the K-31 crowd, but I'm going to put some practice in and at least show respectably in the open sight class.
As for being "flimsy and unreliable" - hogwash. The main reliability problems the SVT faced were operator related. While some soldiers received above average training and got results (ref: Lyudmila Pavlichenko, 309 kills with the SVT sniper variant), the vast bulk of soviet training during the war was little more than "This is your rifle. This is the dangerous end. The enemy is over there. Go to it." And that just doesn't cut it with ANY semi auto weapon.
The Germans loved the SVT, couldn't capture enough of them to keep the front line troops happy. They had training manuals for them, and even an acceptance standard for captured ones. The German G41 was a complete bust, as far as reliability, and so they copied the gas system wholesale from the SVT when they came out with the G43, which says a lot.
In the end, while there aren't as many accessories for the SVT (and never will be, because they practically don't exist in the US, thanks to f#cking Clinton and the "Trade in Military Arms" agreement) as there are for the M14 platform rifles, you're going to be up against a lot of the same problems with both. Both rifles require you to "get to know them", learn their idiosyncrasies, tune and tweak.
You're going to come across SVT lovers and haters on here. For the cost of them, pick one up, clean it, get to know it, fire it, and figure out which camp you'll fall into.
Also, for scope mounting, there are more and more who are coming up with way of mounting the POSP/Dragunov style scopes on them. Requires removing a small amount of wood from the left side of the receiver, and drilling and tapping the side for the POSP rail. Historical value = gone once you go that route, so make sure you know the rifle and whether you figure it's something your going to want to keep and maintain.