I also have the 135 f2.5 Takumar. Its build quality is fine, and since it doesn't seem to be multicoated flare can be a problem, but with SLRs we can see that and change framing. Also it does have a telescoping lens hood. For the curren cost of examples in good shape who can complain? Just wish it had an "A" stop on the diaphragm to ease use on my K5. But on my manual Pentaxes it is happy.
Were they actually sold by Pentax or the US importer ?
I know there's issues in the US with Trade names, sometimes original ipmporters registered the trade names and that makes it very difficult when both sides part company.
It's very strange but I never heward of Takumar (Bayonet) lenses in the UK when they were made although a few turn up on Ebay, but then a lot of Americans are resident here for sort spells as well.
As I understand it they were made and sold by Pentax as a budget range. I know two of the zooms also turned up with Pentax branding (no other difference) as cheap kit lenses.
The 28mm is the same as the late Pentax-M 28mm f2.8 but with different coatings, I have one and it isn't bad around f8. Colours aren't as good as the SMC Pentax 28mm f3.5 (and the Pentax-M 28/3.5) I also own though.
I'm also told that the 135mm f2.8 is a surprisingly decent lens, although the f2.5 doesn't seem hugely popular in reviews. It does seem to be part of what I can only just avoid calling ebay scams though - frequently listed with a high BIN price (as in twice what you'd pay for a good M 135mm f3.5) in the hope that people will mistake it for the SMC Pentax 135mm f2.5 (which is a completely different lens).
I have the Pentax-A 28-80 (and the F version) which were also sold as Takumar-A and -F. Avoid. They're horrible to use and the images are even worse! Mine turned up with a P30n (which I wanted) and is now mostly used as a stand for small items. Covered with a cloth it does a fine job of supporting photographic subjects! There are SMC Pentax 28-80s in both the A and F series which are much better.
Early Takumars were uninspiring, though there were isolated shining stars that are still sought out today. The modern Pentax SMC optics are worlds away from Takumars, though oddities of optical pedigree do exist e.g. Distogon, Biogon heritage designs to account for the limited mirror box real estate.
Dirt making its way into the focusing barrel can be the cause of the scratchy focus. I have handled a Takumar 105mm with this problem very recently.
But if it is labelled Korea, it is certainly not a Takumar: the lenses have always been of Japanese origin.
These aren't the famous Takumars though. The best of the M42 mount Takumars can still hold their own today, the 55mm in its various forms is a particularly popular one.
In the 1980s Pentax brought the name back and used it on a range of cheap K mount lenses as "Takumar Bayonet". These had simplified coatings compared to the full SMC and in some cases were evidently designed to a price rather than a quality. These lenses have nothing in common with the M42 Takumars other than the name.
Gritty focus is usually just that - sand or grit in the helicoil. If it's stiff but smooth you can often improve matters by adding a few drops of light oil and working the focus ring a bit, this should soften the grease again without the hassle of a complete stripdown, clean, and re-greasing (which is a pain as you need to reset infinity focus).