a little about levels, bubbles, and settling
First off, I haven't leveled anything of importance in quite awhile. I have leveled thirty or forty thousand pound chunks of high grade cast iron and long ago leveled a few pool tables.
Anyone leveling their own home table has a huge advantage, they can let it settle. The usual reason a mechanic has to come back and relevel a table isn't because he did a crappy job, the floor or table frame, or slate, moved some as it settled.
Repeating some things but so we are all on the same page:
A piece of slate can be flat without being level. For example, turn a piece of flat slate on it's edge, it can still be flat, it is 90 degrees off of what we consider level! However, a piece of slate that doesn't have at least one smooth surface can never be truly level although it may be acceptably level.
Cheap levels often aren't flat themselves, so trying to decide something else is flat using them will drive you crazy! As has been mentioned already, there are different grades of levels. Once up to the better machinist levels the difference is in the vials, literally! The quality of the glass and the liquid in them. The cheap levels may have alcohol in them and plastic or cheaper glass vials. Ether is used in midgrade levels and I don't know what is used in the best analog levels. The thinner the liquid the more accurate the level can be. Not the only factor but with thick liquid the level can't be accurate. For this discussion alcohol is thick and the liquids used will quickly flash to a gas at room temperature if they are exposed to normal air pressure.
Best to set the table up including slate and rough level it then go away for from three days to a week or more. No idea how long today's thin slates take to settle but letting the floor, the table frame, and the slate stabilize can't be a bad idea unless you are trying to make a buck and need to do a quick job and get on to the next one. If things are badly out of level after settling it may be needed to do a second time. Now get out the nice levels and level the table to the tolerances that make you happy. Once cloth is on and and stretched the better grade precision levels are a waste of time. Those or almost any half decent level can be used to help rough level the table if balls are rolling off.
For those that like to roll balls, a moderate grade 2.25" ball bearing is available for $73 plus shipping from the little yellow hardware store. I suspect it will roll more honestly than any pool ball if rolled slowly. In my misspent youth I considered buying one and painting it white for late night at the bars. I don't know what the ball bearing weighs but I figured it would be an eye opener the first time somebody hit one hard with a cue stick!
Flat and level have little meaning without adding tolerances to the statement. Nothing is flat or level if measured precisely enough, including our instruments! Working to .000025" tolerances was enough to make me crazy and oddly enough was reached by handwork, not precision machinery. Needless to say, that was on something small, not a pool table.
If possible, set up the table, let it rest, relevel, and put on quality cloth. Precision leveling a table then putting on cheap cloth is a waste of time.
Hu