slate that old will probably not be perfect, on mine i could see signs of it being worked. what I did was applied the hard rock putty over the surface to fill any scratches deep enough that I could feel them, most washed off.
on the reverse side of the slate there was a certain amount of porosity. i also found some localized dips and valleys which are simply because it's a natural product like wood so it does have imperfections.
one reason slate is used is because it is very dimensionally stable, if you load it up with tight bolts maybe it can move slightly, you can bend a sheet of glass too. you do not want a situation where it is captive by bolts and being pried or loaded to create a stress point. If you create such a situation it may just get to a point where the stress is high enough and it wont give warning , it will break. one way you could create this situation is by attempting to lift one end of the slate with the alignment pin engaged, you can blow out that section and cause serious damage that you really dont want.
I found my table frame had a bow of about 1/8 " end to end, with the middle being higher. that was good because I was able to level the middle section and then make the ends match. I used some strips of thick heavy vinyl flooring and then paper or card stock when I got closer.
the reason i chose the vinyl is it was fairly thick, stable and if I had any tiny bits like a speck of dirt holding things up it is a bit compressible so that bit of dirt wouldn't be a supporting point like if it were two pieces of metal, slate or glass with no "give" what I did was shift the slate away, stapled it in position , hammered down the staples so they were flush and replaced the slate. I did that as often as needed to get closer.
if you were to start at one end and level that then work on the other slates you may find you need to shim it more than necessary. I used a 6 foot builders level with a machinist level sitting on top of it to get the slates leveled overall. After doing that I start sliding the level around on the slate alone. I could detect minor humps and valleys this way. basically you end up the most accurate when you get down to splitting differences.
one thing that helped me is to place a couple of playing cards every couple feet and put the builders level on that then check if all the cards are tight. I'd then lift the slate and put shims and recheck. aside from getting it as level as possible having the slates on exactly the same plane is important, you don't want any step as the ball rolls from one to the next.
I own a coupleof straight edges used by saw sharpeners, they are simply hunks of high speed steel that have one flat and true edge. I can place those in a vertical position near the gap lie and turn it, if both surfaces are on the same plane I can feel it drag evenly. if one side is higher or if the slates are not level or out of plane with each other. I can tell this way without touching a level. if I try a thin ship anywhere under my straightedge and feel any gap its not correct yet. if I hold it so its pushed tight over part of the slate and there is any gap on the other slate than it's not right yet. Ill lay a flashlight ont he table behind my straightedge, look at thegap of light peeking between, thats agood way to see if the two are in plane.
another interesting way to check if two surfaces are in the same plane is to put a thick piece of glass on the table with a bit of oil under it or maybe another liquid like alcohol will do.
you will then see through the glass and you can press gently on it and see how the oil ( or other liquid) moves around. if one surface is higher it's very easy to see if you try this. Of course dont leave any oil behind. Im not sure you want to satturate the slate pores with oil, just to get the point across that you can check using this technique. It also works f you have two cylindrical shaped pieces and want them parallel. its a neat trick you may want to use.
When you start tightening bolts you should already be close and then you can check with the straightedge , level , etc and you may release the bolts and re-shim until you are happy. Its a think you can rush through in a day or spend several days fussing over to get as perfect as possible. how "picky" do you wan to be? not up to me.
you can check if the slates can be rocked or moved, any solid object can be supported in only 3 points and be level, so being level is part of it, being adequately supported is another. You need both.
I have a small circular bubble level that is very accurate, a machinist level is good at looking at one direction and of course you can turn it, with the round level I can put it anywhere and see which direction the bubble runs to, I found that handy as well.
As you get close you will find that you can put a playing card under one end and then check level and see it's high there, then remove the card and it should go near level, Then put the card under the opposite side now you see the level go the other way, now you know you are accurate to within thicknesses of a playing card, after that you can use paper or something thinner.
some use wood shims. you can use them too if you like. I considered cutting thin wedges.I may still want to go back and put a few thin wedges inthere just to make sure I have enough support points. if you only had the slate supported in the 4 corners and someone were to walk on it then maybe they could break the slate or the slate might droop slightly over time.
I think the quickest way to get there is to just level the 4 corners, get close with that, after that you can put enough shims to make sure you have support over its entire surface or at least at points that aren't too far apart. I'd just say use your judgement on that but realize you want enough points of contact that is's supported mid-span..
you can also take a feeler gauge or playing card and try to stick it between the slate and the rails it sits on. see if it is unsupported anywhere. if so, add shims to make it tight.
I found some shrinkage in my supporting rails , they shrink across the grain. I'd estimate they moved about 1/16" over 8 inches across their grain. , that's typical, due to wood shrinkage over it's 100+ years. basically 2 sheets of vinyl flooring made up for the shrinkage
you can get levels in different accuracies, I'm versed in it because when I bolt together a big machine it has to be very accurately leveled, so it's a similar precision alignment procedure.
to check any spirit level . Find a flat and true surface and get it close to level.
Pick the level up and turn it end for end. if you find the bubble is in the same place , its on.
If you can turn the level and get a different reading with it turned 180, Then you can adjust the spirit level to be more level, trial and error. or split the difference. if its just a builders level it won't have adjustment, its not really a very accurate tool. you can use that to get close, then you need more accuracy.
the accuracy of level is really an infinite measurement, you can go finer until you are splitting differences and detecting humps and valleys and splitting differences. The more serious you are about the game and the table setup. the more time you can spend getting things just as accurate as possible with the tools you have.
a very quick and easy check is to simply put a pool ball on the slate with no cloth, roll it and watch it stop, if you see consistency in which way the ball rolls when it is going very slowly, but moving, then you can use that to decise which is higher, you can get quite accurate with just doing that alone.
You could find that the building moves with the weight of the table, if it's a wood building then the building itself may take time to settle a bit to the weight of the table, so you can recheck later down the road or when you replace the cloth. It's probably a good idea to put the table in place and wait a week for any shifting to ocurr, then do your tweaking as necessary. If the slate is not on yet I'd first check that you have the frame level and evenly supported.
once the slate is level I used the durhams rock hard putty on a wide blade knife, picked up a bead of it on my blade and dragged it evenly across, hopefully there are no low spots to fill but if you must you can adjust for the slight dips and valleys in the slate. unlike bondo which is a thick paste basically, the product thins down like water making it easy for this technique to work. If you dont use the rock hard putty you might subsitute glazing putty which is used to fill imperfections in bondo. it does not need a hardener, just don't apply it thick. I would not use a plastic bondo spreader, use a wide blade steel "putty" knife that you check first and file so it's flat and true.
pool table mechanics who do this every day will no doubt be faster at it, I'd do what you can to try to not make this a hurried situation. if it takes time to get it right , so be it. If you hire a guy you can have a conversation about where to call it good enough.