It seems as if there may be reliability issues with the Gen 4 Glocks. Is this an issue that is more internet myth than truth and if it is indeed true, have these issues been corrected? (from what I've read the issue seems to be related to a newly designed recoil spring system)
There are a few different theories about what isn't working right - the recoil spring, the extractor. I know Glock has shipped different recoil springs for the gen4 19, but I have one of the ones that "don't work right" for other people, and I haven't had a problem. One thing seems pretty certain regarding this - if you have a problem, and call Glock, they'll work to get a part to you to try and get your new gun working like it should.
Is the gen 3 Glock 19 still manufactured?
Like others have said, yep they still make the gen3.
Any advantage of Gen 4 vs Gen 3 or vise versa?
I prefer the size of the gen4 grip. Without any backstrap on the gen4, it's slightly smaller than the gen3 grip - and that fit my hand *perfectly*! The texture of the gen4 grip is like little spikes, vs the more "slippery" grip of the gen3. The gen4 mag release is also ambidextrous and bigger, but you need compatible gen4 mags to swap it out (older mags won't be compatible, but Glock mags are pretty cheap).
I have had no issues with my gen4 Glock 19. It chambers everything fine, and runs fine. However, I did do one small thing (after shooting it stock for a few hundred rounds with no issues):
I changed the trigger bar/trigger assembly to a Glock 17 gen3 version. This was for three reasons:
1) The face of the Glock 17 gen3 trigger is smooth, which I prefer.
2) The trigger bar on the G17 gen3 doesn't have this little "bump" that i found never affected performance, but did smack the rear plate on the slide whenever I broke down the pistol (it would "catch" on the back plate and nick it up, hang up during disassembly a little - the slide wouldn't just "slide" off) and the little bump also somehow made getting the pistol back together occasionally "stick" until I worked out pushing down the safety plunger with the striker pointing downwards, and then putting the slide on.
3) I found it actually improved the trigger pull somehow!
Regarding the slide's finish as someone else mentioned, there are two varieties to finishes for Glocks lately - the slick black finish (which I have on my gen4 19) that people say is far more wear resistant, and then a grayish matte finish that's like parkerizing, which people say wears off faster but Glock says provides a better grip. I don't know if Glock is simultaneously making these finishes, but I seem to remember reading that they switched to the matte gray at this point.