[UncleVanya]

I think that smudge is element separation. The Pentax-M 40mm f2.8 is prone to separation in a pair of elements in the rear lens group. The very thin layer of glue between the lenses breaks down. It looks like something that'll clean right off, or one or more of the other issues suggested.

You could attempt to clean the rear element. You can probably remove the rear group with a lens spanner in the outermost slots, without removing the mount. An improvised lens spanner can be made from an old compass, dividers or needlenose pliers with tips ground to fit the slots.

Oil can evaporate from the grease used to lubricate the focus threads, and end up deposited on the aperture blades and interior lens surfaces on either side of that. Sometimes it is visible on the blades, sometimes not. The grease used by Pentax doesn't usually do that. If you can get the rear element cleaner or notice that the blades close slowly from wide open to f22, it's oil. You can see guides to disassembling other Pentax M series lenses in the Maintenance section. The 40mm is similar to most of those.

If I'm right, my suggestion is to just ignore it. The glue can be dissolved and the elements reglued, but this is generally not worth the trouble for that lens. I have an SMC Pentax-F 70-210 zoom with element separation in the front group, and it doesn't affect shots very much if at all. Here's my attempt to show it in a photo. The cloudiness around the edges sometimes has a gasoline on a puddle look.

I had an F 100 macro that had the same problem. In that element separation the area looked whiter almost like fog. It still worked well no softness but perhaps a bit more like an f4 lens than f2.8.

[MossyRocks]

Lensrentals had a test once where they - if I remember correctly - had a fly in a lens and it had left all sorts of stuff when dying in the lens and it had no or only a very minimal effect on the image.

In most cases yes, but I had gotten some condensation spots on the rear element of my 300/4 and when using it in normal circumstances it wasn't an issue but when I took it out to do some astro shooting it became very apparent that something was wrong/different from the last time as that will show every issue your lens has.

[HoutHans]

Aha, so the rear elements clearly matter. I stand corrected, so thanks for that. I've learned something again.

[MossyRocks]

Aha, so the rear elements clearly matter. I stand corrected, so thanks for that. I've learned something again.

Well my experience is that it mattered when only when using the lens in the most demanding situation, hence under normal circumstance things looked normal and fine. The issue shown only looked a little worse than I had so unless someone is trying to do deep sky object photography with a 40mm pancake they will probably not have any issues.

[UncleVanya]

Aha, so the rear elements clearly matter. I stand corrected, so thanks for that. I've learned something again.

Well my experience is that it mattered when only when using the lens in the most demanding situation, hence under normal circumstance things looked normal and fine. The issue shown only looked a little worse than I had so unless someone is trying to do deep sky object photography with a 40mm pancake they will probably not have any issues.

Try the 0.5cm x 0.5cm square of lens cleaning tissue on your rear element. From what I have seen in the past it will typically cause issues you can see in the viewfinder. On the front element - hard to notice. Focal length and distance to subject may have some impact I don't recall. But a few specs of dust... except for astro I can't imaging that having much impact.

[MossyRocks]

Try the 0.5cm x 0.5cm square of lens cleaning tissue on your rear element.

That would be something rather large, even a .5mm X .5mm bit would be fairly large and I could easily see either causing issues. A few spots from condensation or finger print less so, unless really pusing the lens's capabilities. Specks of dust aren't a real big concern in astro images as they cover only a tiny portion of the area and one is typically using telephotos so they become less of a concern. Dust on the sensor is a nightmare though with astro shots. What I saw with the dried condensation spots was what appeared to be some bad coma in a set of astro shots.

[Mercifulfate]

Take it apart and clean it.