What a lot of great information in this thread!
I found my old 1970s era Model 25 in my mother's attic when cleaning out her house after she passed. I was eager to see how it would compare to my newer and very accurate Daisy 35. It was a let-down... I had memories of doing some accurate shooting with that old Daisy, but either my memory was a bit off or the Daisy hadn't aged well.
I guess she needs a little TLC!
Hi "desmobob" if you don't mind letting me make a few suggestions & ask a question or two.
Many of us that basically started out when we were young with BB guns I believe in most cases shot a lot of stuff at closer distances than we remember & what we've now forgotten is we shot so much stuff that we really didn't use the sights, we were able to just able to instinctively eye down the barrel with both eyes & point & shoot, I myself had forgotten that.
So, in probably 7 of the 9 older M-25's I've acquired & that includes the one I personally had in the early 70's the rear sights were so twisted & bent that it really wasn't possible to have been using them
So, in my older age & my older eyes & script glasses, & the short youth stocks on those older guns I can't really focus on the sights especially the V-notch sight.
[I'm trying to work out a way to short cut this story book]
When I first started working on these old M-25's I was setting up test targets in the house with towels in a box to catch BB at close distances, & I was using multi layers of cut up Pizza box tops for penetration test. The first one I worked on when I started was so bad that it wouldn't shoot through a single layer (I stack them in 8 layers & use rubber bands to hold them together), & shoot at them at say 6 or 8 feet. So, when I work though the gun they may end up shooting maybe 5-6 layers (without any modifications) So, if you haven't tested that old gun for reasonable power then that may be a accuracy issue.
Next is the old shot tube's did not wear well over hundreds of thousands of cycle BB's, so a new model replacement shot tube will likely help a good bit, they're a better design overall.
Now let me get back to where I started in this post.
Also, I'm not meaning in any way that you don't know how to shoot a gun, based on the info I seen in your profile you may even be an "Expert" in shooting regular firearms.. So, I'm just covering this encase you've forgotten the rule of grip shooting a springer gun.
The recoil of a springer gun happens within the gun before the bb exits the muzzle, the energy (recoil) can not be controlled by any actual means of just holding the gun (grip) & trying to do so will make accuracy of most of them worse. So, its best to not try & control the recoil & let the spring do what it does. All of the action from the spring is directly in prefect horizonal alignment with the gun, but if you try to control it, which isn't possible then the energy released from the spring is transferred more into an erratic pattern at the muzzle, & it all happens before the bb exits the muzzle.. (That's just incase you didn't know that or maybe forgotten). So, its best to just let the front of the gun REST on say the palm of your hand & not grip it at all.
instinctively shooting these when we were kids is something as a kid I never even thought about, I just did it.
So, working through all my M-25 projects some for actual use & some just for collecting, meaning some I've extended the stocks to more of an adult length, & did a little Hot Rodding to them. I've done a good bit of test firing all of them. (I'm getting to the point, I promise

) So I step out on my little back porch with one gun I'd been working on just to cycle some bb's through it, it had the factory length youth stock on it so I didn't even give the sights a thought, I was just going to shoot into the ground at maybe 15 feet or so at nothing. So, that's what I did, then I noticed a few leaves laying around so, I just point at one & shoot & I saw the blades of grass move from the impact just a couple inches away, so, I pop off another point & shoot & hit the leaf. Not realizing it yet I point & shoot at another leaf & I hit it, so, I'm firing away at these maybe 2"-wide 3"-long leaves & I'm hitting way more than I'm missing & the misses are CLOSE. Then after doing this several times, I had a flash back! it hit me, this is what I was doing when I was a kid for a great deal of my shooting. Try it some time, you may get a chuckle out of it, I did.
To sum this up.
Its been stated by people in the know, that even a little bit of oil in the shot tube barrel (& dirt) can cause accuracy problems, rig up a way (if you haven't yet) to drag a small patch through the barrel, even its its just a length of button thread tied to a hair pin clip will work.
If you may have been (??) using the wrong grip correcting that will help, the M-25 is one that as best that I can tell it don't like the front of the gun HELD accuracy wise.
Locating a newer style shot tube is likely to be an improvement too.
Also, if you can post a picture of that old M-25, yes we expect it to look VERY well USED
Here's my ragged out M-25 from the late 60's early 70's this old gun has likely had millions of bb's cycled through it, & I fixed it & got it working again & pretty darn good.
This picture is before I removed the 1970 electrical tape & patched the stocked..
Here the gun had been restored back to "Working Order" but cosmetically its as it was when we outgrew the bb gun age (it was retired)
When I started working on this old gun it cocked & popped, but it didn't' have any power & the shot tube didn't have much control of feeding bb's so several at time might just roll out the end of the barrel, it was a tired old gun for sure

So, the shot tube was well..... SHOT..
But after I got on the inside of it I found the main reason for it lack of power, & that was the tip of the air tube was badly deformed (battered) so much so that it only a tiny pin hole remained to pass air through.
When I decided to take a picture of the damaged air tube I had already starting working a little bit to open the end of it up.