Yes, accuracy does improve because as already mentioned as more slits are used, or as there is less space between multiple slits, the width between fringes increases therefore making it easier to get more accurate and precise measurements of the fringes. This can be better understood by looking at this equation (the name escapes me):
(d)(sin x) = (WL)👎
where d is equal to the slit spacing, x is equal to the angle between the fringes and the slit, WL = wavelength of light, and n is the fringe number where the central fringe is equal to 0.
If you were to hold (WL)👎 constant:
(d)(sin x) = K
Then as d were decreased (the spacing between slits), the angle must increase to keep it equal to that constant K. The larger the angles between the fringe and the slit, the farther the distance between the fringe. The opposite is also true: as the distance between fringes is increased, the smaller the angles, the shorter the distance between fringes, the harder it is to measure.
I always remembered this by remembering the equation... but pretty much it is all based on constructive and destructive interference and how light has properties like that of waves. Where the light waves from each slit are in phase, constructive interference is observed and you get a bright spot. Where the light waves from each slit are "perfectly" out of phase, destructive is observed and thus a dark spot appears. By perfectly out of phase I mean where the max of one wave is corresponds to the minimum of the other. It would be much easier to explain this on paper, but I am sure your text has some thing about this.
So anyways, if the slits are moved closer together, it takes a longer distance for the waves from each slit to be in phase. I can't really figure out how to in words... I would probably have to go find a text book. And I should be sleeping. Well, hope this helps.
