I don't see any obvious indication of disease or concerns other than the browning. That brown root is firm, not squishy, right?
I think monsteras needs a pretty good amount of light for a houseplant, but it's possible that as the season changes and the light is getting stronger, your monstera is now getting a bit TOO much light, which is crisping up the leaves. So maybe try to find a spot with just a bit less light?
Also, I think I see two cuttings in that glass? If so, I would put the two cuttings in two separate glasses of water. That way, if one glass happens to get infected with some kind of nasty root-eating microbe (which it looks like you're changing the water frequently, so that shouldn't happen, but just in case), you don't lose both cuttings.
If the brown bits on the leaves were wet frequently, they'd be an infection risk, but since they're dry, they probably aren't. So the choice to trim or not to trim probably has more to do with aesthetics than with plant health. I'd probably trim the brown bits that are sticking out (leaving a thin margin of brown rather than risk damaging new tissue), but wouldn't trim into the leaf.
But these are my hunches based on relatively modest experience, so I hope you get a second opinion.