Scope mount and repeatability stories:
01 - My first scope, purchased Jan 2013, was an "Aim Sports" 3-9x Mil Dot Ill Ret, cheap-O scope. I got it purposely as a "learning scope" ... not wanting to get a real one and mess it up. The only rifle I had then was the Sig 7.62. I had lots of problems ... the scope kept comming loose ... and that's how I said it ... and that's how I thought it ... I blamed the "scope" ... but actually those problems had nothing to do with the scope. They had everything to do with the scope mount. The scope mount was badly designed and badly built ... but it also had to do with me ... while this scope did not say it would only work on rimfire rifles ... with a little judgment I was able to realize that was the case. So it wasn't the scope, it was the scope mount. Scope mounts are VERY important. Some shooters (as I did at first) .. think of a scope mount (if they think at all) as being just a widget that holds the scope. But the scope mount has to latch on to the rail and the scope both to prevent any "extra" movement ("extra" being not caused directly by recoil) which could damage the optic. A loose mount could allow the scope to "slam around" in reaction to the recoil which is not a good thing. Recoil is bad enough, extra slamming around in reaction to recoil is worse. Acceleration is one thing ... jerks are another ... lots of jerks quickly are another.
BTW, the scope sucked also ... terrible glass ... but that was a separate issue. I learned a lot from my "learning scope". I learned scope monunts were important, I learned bad glass was bad and I learned cheap scopes suck .... it was a great learning experience. It cost me $189 ... I included it when I sold my first .22LR (Mossberg 715T) and got 1 cent back out of 3 spent on the combined deal ... so net/net it cost me $126 to learn what I learned.
02 - My next scope was an L&S 3.5-10x TMR Ill Ret and I still use that scope. These days it is the designated day scope for the 5.56(18) which is similar to a Mk12 SPR so putting the L&S 3.5-10x on there is appropriate as the Mk12 have had similar optics on them. But in 2013 I ran this scope on the Sig 716 ... also appropriate because M110 ran this exact scope in the military (which I did not know when I bought).
My first NV was ATN PS-22 and I ran that on the L&S 3.5-10 on the Sig762. At first I ran it with the "direct scope mount" ... which tensions on to the objective bell of the day scope. Leupold said I could torque this up to 30 inch/pounds ... I used 25 ... after six months the scope mount sleeve cracked and it cost $80 to replace it. I also called ATN and they told me not to torque, but to finger tight. I had tried that, but then the mount would come loose. But ATN also recommended using rail attach instead of direct scope attach and I've been doing that ever since. Subsequently others have said "never use direct scope attach" ... I still have the capability and could do it in a pinch ... but I have not done it once since ATN said not to.
So then I was rail attaching the PS-22 ... and the PS-22 mount is a weakness of the system. It is tough to get the tension balanced between the two tensioners ... I am currently trying to get the monunt replaced. So having the monunt come loose after 10-20 rounds, means I have to check it all the time. Mounts are important.
03 - My next clip on was (is - I still have it) the COLR. These days I mostly run that on the .338LM bolt gun, because it is the only thing that can take the recoil. That mount sucks also. Each time I move it to a different rifle, I have to change the tension, hence I don't move it around much any more. And even on any rifle, it is either too tight ... can't close the levers all the way properly ... or too loose ... either way ... it winds up flopping around after a few rounds ... I run it too tight ... so at least it will hold for a round or so. Waiting for bobro mount for this. Supposedly bobro mount with "auto-tension" to match the rail ... that magic will be extremely welcome!
Point is ... mounts are important.
04 - Most people will tell you when you mount a scope, if there is any play, push it forward, to remove the play. That is logical, maybe even "common sense" ... since the rifle will recoil to the rear, anything attached to the rifle that can move (play) will slide forward ... some of the "extra" movement mentioned earlier ... so mounting the scope as far forward in the rail slot minimizes this "extra" movement.
I add a second part to that rule. If there is any lateral play I slide the scope as far to the left as possible. This is arbitrary, I could slide it to the right. But for repeatability I want to be consistent, so my rule is "to the left".
I just remounted L&S 6.5-20x TMR scope on .338LM bolt gun, which is now entering its season, so we will soon see how "repeatble" this mount is. This is an ADM mount, so I am hopeful!
05 - My newest scope is Vortex 1-6x MRAD, with another ADM mount. I messed with the tension a lot to try to get it "perfect" ... not "good enough" but "perfect"

... and I think it is as good as it can be. It mounts with no lateral play ... I slide it forward and latch it down and so far I cannot tell any POI shift. But this scope is on .22lR and so far have not shot this setup beyond 100yds. But I expect to be able to get out to 300yds+ with this setup ... this is new CMMG upper replacing last years PTA upper.
06 - The tension on the ADM mounts is easy to adjust with no tools ... much harder for the COLR and Zeus mounts, but easier when they are new. Theory is they degrade over time. The new Bobro mounts (the trucks have been rolling towards us for months, bringing us these new magic mounts, but none have arrived in my foxhole yet

) are supposed to auto-tension. And this should maximize repeatability even on different rifles. Once the trucks actually arrive and unload, we can start testing these mounts on COLR, Zeus, etc. It should be a great day.
07 - Rail clips. I use Larue rail clips .. little pieces of plastic that clip on to one rail section to mark that section. In the dark, you need to be able to go by feel alone. These things work. I can put the apollo back in the same spot in seconds without using my eyes, because of a rail clip. They are 72 in a pack, I don't recall the cost. They are also good markers for day scopes and stuff. The use of rail clips ensures the optics go back in the same rail position each time, thus enhancing repeatability.