According to Huygens' principle, each wavefront is an infinite superposition of the secondary wavelets created by the previous wavefront. So if we take an infinite number of slits and light undergoes interference, I expect to see general illumination and not bands or fringes. What do you guys say? The width and distance between the slits is finite.
I think the answer is not the uniform brightness. In fact you can compute the N slit experiment with finite width for the slits. For a supposed 0-width, you'll get an interference pattern that is getting sharper and sharper :
Then, if you suppose a non zero width, you'll get an enveloppe on that pattern :
(This is the case of 2 wide slits)
Finally, if N goes to infinity, you'll get a "Dirac comb" topped by the pattern due to the width of the slits. Still, in reality, you cannot make light go through this infinite number of slips (because of the infinite amount of energy it would require to produce such light), so in the end I guess the pattern would be as sharp as you manage to light up more slits.